Patients must have histologically or cytologically confirmed relapsed/refractory CD low (< %) TCL:\r\n* Peripheral TCL not otherwise specified (PTCL NOS)\r\n* Angioimmunoblastic T cell lymphoma (AITL)\r\n* Hepato-splenic T cell lymphoma (HTCL)\r\n* Adult T cell leukemia/lymphoma (ATLL)\r\n* Enteropathy associated T cell lymphoma (EATL)\r\n* Natural killer (NK) T cell lymphoma (NK/TCL)\r\n* Transformed mycosis fungoides Patients must have histologically confirmed mantle cell lymphoma (MCL)\r\n* Please note: measurable disease is not required, but will be followed if it exists Participant must have a histologic diagnosis of a mature B cell lymphoma (e.g., Burkitt lymphoma/leukemia, atypical Burkitt lymphoma, diffuse large B-cell lymphoma, mediastinal large B-cell lymphoma, mature B-cell lymphoma not-otherwise specified [NOS]) as defined in the World Health Organization (WHO) classification PARTICIPANTS FROM COLLABORATING SITES PARTICIPATING IN BIOLOGICAL OBJECTIVES ONLY: Participant must have a histologic diagnosis of a mature B cell lymphoma (e.g., Burkitt lymphoma/leukemia, atypical Burkitt lymphoma, diffuse large B-cell lymphoma, mediastinal large B-cell lymphoma, mature B-cell lymphoma NOS) as defined in the WHO classification Histologic diagnosis other than a mature B-cell lymphoma as defined in the WHO classification Systemic lymphoma Peripheral T-cell lymphoma-not otherwise specified (PTCL-NOS); Natural-killer/T-cell lymphoma (NKTL) Fluorodeoxyglucose (FDG)-avid lymphoma (that is [i.e.], PET-positive lymphoma) Biopsy proven plasmablastic lymphomas, or peripheral T cell lymphoma (with the exception of anaplastic lymphoma kinase positive [ALK+] type in first or second complete remission) (timeline months prior to enrollment) Cutaneous T cell Lymphoma (CTCL) NHL SA expansion: Mature B-cell NHL with the following histologies: primary mediastinal lymphoma, DLBCL, and B-cell lymphoma not specified that is R/R to standard therapy and for whom standard treatments are contraindicated or unavailable Patients must have a histological diagnosis of any of the following (all stages allowed):\r\n* Diffuse large b-cell lymphoma (DLBCL) (including transformation from a previously indolent non-Hodgkin lymphoma [NHL], so long as no prior systemic treatment was given for the indolent NHL)\r\n* B-cell lymphoma, unclassifiable\r\n* Burkitt lymphoma\r\n* MYC+ plasmablastic lymphoma by histology Angioimmunoblastic T-cell lymphoma (AITL) Enteropathy-associated T-cell lymphoma Extranodal natural killer (NK) T-cell lymphoma, nasal type Hepatosplenic T-cell lymphoma Peripheral T-cell lymphoma, no otherwise specified (NOS) Precursor T-cell lymphoma or leukemia Adult T-cell lymphoma/leukemia (ATLL) Histologically confirmed diagnosis of PTCL (using the most recent edition of the World Health Organization [WHO] Classification of Tumors of Hematopoietic and Lymphoid Tissues as guidance) including: \r\n* Anaplastic large cell lymphoma, anaplastic large cell kinase (ALK)-negative \r\n* Angioimmunoblastic T-cell lymphoma \r\n* Enteropathy-type T-cell lymphoma\r\n* Hepatosplenic gamma-delta T-cell lymphoma \r\n* Peripheral T-cell lymphoma, unspecified (not otherwise specified [NOS]) \r\n* Transformed mycosis fungoides\r\n* Subcutaneous panniculitis-like T-cell lymphoma. \r\n* NOTE: patients with adequate archived (well-preserved, formalin-fixed) biopsy tissue remaining will be required to submit a portion for exploratory studies; this is not optional if tissue is available; however, lack of adequate tissue for exploratory studies will not preclude patients from participating Patients with a diagnosis of any of the following are not eligible:\r\n* Anaplastic large cell lymphoma, ALK-positive \r\n* Adult T-cell lymphoma/leukemia (ATLL)\r\n* Anaplastic large-cell lymphoma, primary cutaneous type\r\n* Precursor T-lymphoblastic lymphoma/leukemia\r\n* Mycosis fungoides/Sezary syndrome (except transformed mycosis fungoides [MF])\r\n* Natural killer (NK)-cell leukemia\r\n* T-cell granular lymphocytic leukemia\r\n* T-cell prolymphocytic leukemia Histologically-confirmed B-cell non-Hodgkins lymphoma (mantle cell lymphoma, follicular lymphoma, small lymphocytic lymphoma/chronic lymphocytic leukemia, marginal zone lymphoma, diffuse large B-cell lymphoma, and lymphoplasmacytic lymphoma) Patients with T-cell or B cell lymphoblastic lymphoma confirmed by conventional immature T- or pre B cell markers even if the bone marrow is not involved are also eligible Patients with newly diagnosed Group A (low risk) lymphoma. Patients with Group B (intermediate risk) if classified as Murphy Stage III/IV and diagnostic LDH > XULN and patients with primary mediastinal B-cell lymphoma (PMBL). Patients must have histologically documented metastatic solid tumors which have progressed after one line of therapy, or lymphoma which has progressed after all Food and Drug Administration (FDA)-approved therapy; this trial will enroll a minimum of lymphoma patients Non-Hodgkins lymphoma (NHL) or Hodgkins lymphoma (HL) beyond first remission Falls under one of the following subtypes of CD positive non-Hodgkin lymphoma (defined as >= % positive staining by immunohistochemical staining or flow cytometry by local lab):\r\n* High-grade B-cell lymphoma, with MYC and BCL and/or BCL rearrangements (DHL)\r\n* DLBCL or high-grade B-cell lymphoma NOS or B-cell lymphoma unclassifiable with features intermediate between Burkitt lymphoma and diffuse large B-cell lymphoma with MYC and BCL protein over-expression by immunohistochemical (IHC) staining as defined by MYC expression in >= % of cells and BCL positivity >= % (DOL)\r\n* Transformed lymphoma with MYC rearrangement by fluorescence in situ hybridization (FISH) or over-expression by IHC, as above\r\n* CD positive mature T-cell lymphoproliferative disorder Histologically confirmed mature peripheral T-cell or natural killer (NK)-cell lymphoma per World Health Organization (WHO) classification, including: \r\n* Anaplastic lymphoma kinase (ALK)-positive anaplastic large cell lymphoma (ALCL) with international protein index (IPI) of or higher (must have stage III-IV disease)\r\n* ALK-negative ALCL\r\n* PTCL-not otherwise specified (NOS)\r\n* Angioimmunoblastic T-cell lymphoma (AITL)\r\n* Adult T-cell lymphoma/leukemia (ATLL) \r\n* Enteropathy-associated T-cell lymphoma (EATL)\r\n* Hepatosplenic T-cell lymphoma INCLUSION - PROCUREMENT: Referred patients will initially be consented for procurement of blood for generation of the transduced ATL; eligibility criteria at this stage include:\r\n* Diagnosis of recurrent T-cell acute lymphoblastic leukemia (T-ALL), T-cell acute lymphoblastic lymphoma (T-LLy), or T-non-Hodgkin lymphoma (T-NHL, including angioimmunoblastic T-cell lymphoma [AITL], enteropathy-associated T-cell lymphoma [EATL], monomorphic epitheliotropic intestinal T-cell lymphoma [MEITL], peripheral T-cell lymphoma [PTCL] not otherwise specified [NOS], anaplastic large cell lymphoma [ALCL] adult T-cell leukemia/lymphoma, T cell prolymphocytic leukemia with symptomatic disease, extranodal natural killer [NK]/T cell lymphoma, mycosis fungoides/ Sezary syndrome stage IIb or higher)\r\nAND\r\n* suitable for allogeneic hematopoietic stem cell transplant (HSCT)\r\n** with confirmation of an identified eligible allogeneic (allo)-HSCT donor by a Foundation for the Accreditation of Cellular Therapy (FACT) accredited transplant center AND \r\n** with confirmation that the center plans to proceed with transplant if CD.CAR treatment induces a complete remission\r\n* For T-NHL subjects, eligibility will be confined to disease stages where allogeneic HSCT is indicated INCLUSION - TREATMENT: Diagnosis of recurrent T-cell acute lymphoblastic leukemia (T-ALL), T-cell acute lymphoblastic lymphoma (T-LLy), or T-non-Hodgkin lymphoma (T-NHL, including angioimmunoblastic T-cell lymphoma [AITL], enteropathy-associated T-cell lymphoma [EATL], monomorphic epitheliotropic intestinal T-cell lymphoma [MEITL], peripheral T-cell lymphoma [PTCL] NOS, anaplastic large cell lymphoma [ALCL], adult T-cell leukemia/lymphoma, T cell prolymphocytic leukemia with symptomatic disease, extranodal NK/T cell lymphoma, mycosis fungoides/ Sezary syndrome stage IIB or higher) AND\r\n* suitable for allogeneic hematopoietic stem cell transplant (HSCT) \r\n** with confirmation of an identified eligible allo-HSCT donor by a FACT accredited transplant center AND\r\n** with confirmation that the center plans to proceed with transplant if CD.CAR treatment induces a complete remission\r\n* For T-NHL subjects, eligibility will be confined to disease stages where allogeneic HSCT is indicated Biopsy proven aggressive B-cell Non-Hodgkin Lymphoma (B-NHL), including diffuse large B-cell lymphoma (DLBCL) not otherwise specified (NOS), follicular lymphoma Grade B, PMBCL, T-cell rich B-cell lymphoma, or DLBCL that represents transformation of indolent non-Hodgkin's Lymphoma (NHL), (including follicular, marginal zone, and lymphoplasmacytoid lymphoma) excluding chronic lymphocytic leukemia or Hodgkin Lymphoma. The following histologies are not eligible: lymphoma History or diagnosis of mantle cell lymphoma or anaplastic large cell lymphoma. Patients with systemic T cell lymphoma of any stage and any subtypes; patient must have had at least one standard chemotherapy and measurable disease at the time of enrollment Mantle-cell lymphoma, prolymphocytic leukemia: Eligible after initial therapy in >= CR or >= PR Biopsy confirmed low-grade B-cell lymphoma, including grade , , or A follicular lymphoma, marginal zone lymphoma, small lymphocytic lymphoma, lymphoplasmacytic lymphoma, or indolent mantle cell lymphoma; patients may be newly diagnosed or previously treated Patients must have relapsed (first or greater relapse) or refractory lymphoma with:\r\n* Lymphoblastic lymphoma or peripheral T-cell lymphoma\r\n* Histologic verification of disease at original diagnosis or subsequent relapse\r\n* Evaluable or measurable disease documented by clinical or radiographic criteria or bone marrow disease present at study entry\r\n* Patient may have CNS status if other sites of leukemia or lymphoma involvement are present Adults with histologically proven solid malignancy, high-grade lymphoma or low-grade lymphoma Histologically confirmed mantle cell lymphoma (confirmation of cyclin D positivity on diagnostic biopsy) Patients with peripheral T-cell lymphoma (including but not limited to peripheral T-cell lymphoma, not otherwise specified [PTCL-NOS], angioimmunoblastic T-cell lymphoma, anaplastic large T-cell lymphoma). Patients with mycosis fungoides with large cell transformation with measurable disease is eligible. Patients must have histologically or cytologically confirmed relapsed and/or refractory B-cell lymphoma confirmed by the Laboratory of Pathology, National Cancer Institute (NCI), as follows:\r\n* Aggressive B-cell lymphoma: includes diffuse large B-cell lymphoma (DLBCL) and subtypes, transformed lymphoma, Burkitt lymphoma, as well as high-grade B-cell lymphoma with MYC and/or BCL and/or BCL rearrangement(s)\r\n* Indolent B-cell lymphoma:\r\n** Chronic lymphocytic leukemia (CLL)/small lymphocytic lymphoma (SLL) is excluded\r\n** Mantle cell lymphoma (MCL) is excluded\r\n* NOTE: patients with known active central nervous system (CNS) lymphoma are not eligible Phase Part: Patients with pathologically confirmed advanced stage B-cell NHL (Ann Arbor stage or ) for whom R-CHOP is considered appropriate therapy; newly diagnosed DLBCL, newly diagnosed low grade B cell NHL, and previously treated low grade B cell NHL patients in first relapse after a prior treatment with non-anthracycline containing chemotherapy are allowed; double hit and transformed diffuse large B cell lymphoma are allowed\r\n* Allowed low grade B cell lymphomas will include follicular lymphoma any grade, marginal zone lymphoma including mucosa-associated lymphoid tissue (MALT) lymphoma, indolent mantle cell lymphoma and Waldenstrom's macroglobulinemia Mature B-cell lymphoma\r\n* Follicular lymphoma and other indolent lymphoma\r\n** In >= second CR/PR\r\n* Diffuse large B-cell lymphoma\r\n** In >= CR or >= PR\r\n** A high intermediate or high international prognostic index (IPI) (>= for age-adjusted IPI or >= for IPI) at diagnosis and double-hit or triple-hit lymphoma will be eligible in first CR\r\n** Transformed lymphoma from follicular lymphoma (FL) (or other indolent lymphoma) or chronic lymphocytic leukemia will be eligible if chemosensitive and bone marrow is negative\r\n* Mantle cell lymphoma\r\n** In first or greater CR or PR\r\n* Burkitts/Burkitts like\r\n** All patients except localized lymphoma will be eligible any time after initial therapy (after achievement of first complete remission), or in partial remission if they fail to achieve CR\r\n** Patients with localized (stage I or Ziegler stage A) will be eligible only if they fail to achieve CR or after relapse Relapsed or refractory T-cell lymphoma (TCL) biopsy-proven =< months prior to registration, including the following subtypes:\r\n* Peripheral T-cell lymphoma, not otherwise specified\r\n* Anaplastic large cell lymphoma, anaplastic lymphoma kinase (ALK) negative, primary systemic type\r\n* Angioimmunoblastic T-cell lymphoma\r\n* Extranodal natural killer (NK)/T-cell lymphoma, nasal type\r\n* Adult T-cell lymphoma/leukemia (human T-lymphotropic virus [HTLV]+)\r\n* Blastic NK-cell lymphoma\r\n* Enteropathy-associated T-cell lymphoma\r\n* Hepatosplenic gamma delta T-cell lymphoma\r\n* Transformed mycosis fungoides\r\n* T/NK-cell lymphoma, unclassifiable Patients must have Hodgkin lymphoma, anaplastic large cell lymphoma, peripheral T-cell lymphoma not otherwise specified, diffuse large B-cell lymphoma not otherwise specified, primary mediastinal B-cell lymphoma, gray zone lymphoma, enteropathy-associated T-cell lymphoma, or extranodal natural killer (NK)/T-cell lymphoma, nasal type Previously untreated participants with cluster of differentiation (CD)-positive DLBCL, including one of the following diagnoses by World Health Organization (WHO) classification of lymphoid neoplasms: DLBCL, not otherwise specified (NOS) including germinal center B-cell type, activated B-cell type; T-cell/histiocyte-rich large B-cell lymphoma; Epstein-Barr virus-positive DLBCL, NOS; anaplastic lymphoma kinase (ALK)-positive large B-cell lymphoma; human herpesvirus- (HHV)-positive DLBCL, NOS; High-grade B-cell lymphoma with MYC and B-cell lymphoma (BCL) and/or B-cell lymphoma (BCL) rearrangements (double-hit or triple-hit lymphoma); High-grade B-cell lymphoma, NOS History of indolent lymphoma B-cell lymphoma, unclassifiable, with features intermediate between DLBCL and classical Hodgkin lymphoma (grey-zone lymphoma) Patients with B-cell lymphoma who are candidates to autologous stem-cell transplantation: \r\n* Primary refractory or relapsed diffuse large B-cell lymphoma in response to salvage treatment\r\n* Primary refractory or relapsed follicular lymphoma or other indolent B-cell histology in response to salvage treatment\r\n* Chemosensitive mantle-cell lymphoma in first or later line of treatment PHASE I: Histologically confirmed B-cell NHL with any of the following subtypes: DLBCL, mantle cell lymphoma (MCL), FL, marginal zone lymphoma (MZL) and lymphoplasmacytic lymphoma/Waldenstroms macroglobulinemia (LL/WM), Burkitts lymphoma (BL); patients with histological transformation to DLBCL from indolent lymphoma, primary mediastinal lymphoma and grey zone lymphoma are eligible CUTANEOUS T-CELL LYMPHOMA (CTCL) ONLY PERIPHERAL T-CELL LYMPHOMA (PTCL) ONLY Phase I portion of the study: The following types of NHL as documented by medical records and with histology based on criteria established by the World Health Organization (WHO):\r\n* Mantle cell lymphoma (MCL)\r\n* Follicular lymphoma (FL) - grades -a\r\n* Lymphoplasmacytic lymphoma (LPL)\r\n* Marginal zone lymphoma (MZL)\r\n* CLL in Richters transformation\r\n* B-cell prolymphocytic leukemia Refractory to chemotherapy lymphoma Relapsed large-cell lymphoma, mantle-cell lymphoma and Hodgkin lymphoma that is chemotherapy sensitive and has failed or ineligible for an autologous transplant Lymphoplasmacytic lymphoma is eligible after initial therapy if chemotherapy sensitive Large cell lymphoma, mantle cell lymphoma and Hodgkin disease that is progressing on salvage therapy Lymphoplasmocytic lymphoma Mantle cell lymphoma ([MCL] with the exception of aggressive MCL, defined as Ki > %, or blastoid histology) PART I: Histologically confirmed B-cell NHL with any of the following subtypes: diffuse large B-cell lymphoma (DLBCL), mantle cell lymphoma (MCL), follicular lymphoma (FL), marginal zone lymphoma (MZL) and lymphoplasmacytic lymphoma/Waldenstroms macroglobulinemia (LL/WM), Burkitts lymphoma (BL); patients with histological transformation to DLBCL from indolent lymphoma, primary mediastinal lymphoma and grey zone lymphoma are eligible PART IB: Histologically confirmed B-cell NHL:\r\n* Group : with only de novo DLBCL,\r\n* Group : with only FL of grade , or a\r\n* Group : with only MCL with t(;) or overexpression of cyclin D\r\n* Group : all other NHL including MZL, LL, WM, BL, primary mediastinal B cell lymphoma (PMBCL), gray zone lymphoma (GZL) and patients with histological transformation to DLBCL from indolent lymphoma are eligible Primary disease of hematologic origin, lymphoma, or small cell cancer Measurable or assessable lymphoma Patients must have a diagnosis of prior treated diffuse large b-cell lymphoma, mantle cell lymphoma, transformed lymphoma, follicular lymphoma (any grade), small lymphocytic lymphoma, marginal zone lymphoma, or Hodgkin lymphoma who do not have curative treatment options Lymphoplasmacytic lymphoma, mantle-cell lymphoma, prolymphocytic leukemia are eligible after initial therapy if chemotherapy sensitive Large cell lymphoma, mantle cell lymphoma and Hodgkin disease that is progressing on salvage therapy Patients diagnosed with a leukemia or lymphoma as follows:\r\n* Chronic or acute leukemia forms of HTLV- associated adult T-cell leukemia;\r\n* Peripheral T-cell lymphoma (angioimmunoblastic, hepatosplenic, or not otherwise specified); or,\r\n* Cutaneous T-cell lymphoma stage III or IV with circulating monoclonal cells (B or B) and/or erythrodermia (T)\r\n* T-cell prolymphocytic leukemia (T-PLL)\r\n* NOTE: Diagnosis must be validated by the Pathology Department, National Cancer Institute (NCI) Patients must have been refractory or relapsed following front line therapy for adult T-cell leukemia (ATL); those with cutaneous T-cell lymphoma (CTCL) or peripheral T-cell lymphoma (PTCL) who have CD+ disease must have progressed during or after treatment with brentuximab vedotin, or are unable to receive treatment due to allergy or intolerance Lymphoplasmacytic lymphoma, mantle-cell lymphoma, prolymphocytic leukemia, natural killer (NK) cell malignancies are eligible after initial therapy in CR+ or partial remission (PR+) No prior treatment for lymphoma Malignancy criteria:\r\n* Patients with the following malignancies are potentially eligible: any B-cell lymphoma and chronic lymphocytic leukemia (CLL); patients with indolent malignancies that have transformed to diffuse large B-cell lymphoma are eligible\r\n* Clear CD expression must be uniformly detected on % or more of malignant cells from either bone marrow or a leukemia or lymphoma mass by flow cytometry or immunohistochemistry; these assays must be performed at the National Institutes of Health; it is preferable but not required that the specimen used for CD determination comes from a sample that was obtained after the patients most recent treatment; if paraffin embedded unstained samples of bone marrow involved with malignancy or a lymphoma mass are available, these can be shipped to the National Institutes of Health (NIH) for CD staining; otherwise, new biopsies will need to be performed for determination of CD expression\r\n* Diffused large B-cell lymphoma (DLBCL) patients must have received at least two prior chemotherapy-containing regimens at least one of which must have contained doxorubicin and a monoclonal antibody; follicular lymphoma patients must have received at least prior regimens including at least regimen with chemotherapy; all other lymphoma and leukemia patients must have had at least prior chemotherapy-containing regimen; all patients with CLL or small lymphocytic lymphoma must have had prior treatment with ibrutinib or another signal transduction inhibitor\r\n* Patients must have measurable malignancy as defined by at least one of the criteria below\r\n** Lymphoma or leukemia masses that are measurable (minimum . cm in largest diameter) by computed tomography (CT) scan is required for all diagnoses except CLL; all masses must be less than cm in the largest diameter\r\n** For a lymphoma mass to count as measurable malignancy, it must have abnormally increased metabolic activity when assessed by positron emission tomography (PET) scan\r\n** For CLL and lymphoma with only bone marrow involvement no mass is necessary, but if a mass is not present, bone marrow malignancy must be detectable by flow cytometry in lymphoma and CLL Diagnosis of either cutaneous T-cell lymphoma; T-prolymphocytic leukemia; T-large granulocytic leukemia; T-lymphoblastic leukemia/lymphoma; or peripheral T-cell lymphoma, natural killer/T-cell lymphoma for whom allogeneic stem cell transplantation is indicated Participants with primary mediastinal B-cell lymphoma (PMBCL) Only line of previous anti-lymphoma therapy is allowed and not currently receiving any other agent that would be considered as a treatment for the lymphoma; patients must be >= weeks from prior anti-lymphoma therapy; the use of steroids and/or rituximab up to week prior to registration for management of symptoms is allowed Pathologic diagnosis of one of the following:\r\n* For dose escalation:\r\n** Confirmed diagnosis of peripheral T-cell lymphoma (PTCL) or angioimmunoblastic T-cell lymphoma (AITL) that is refractory to at least one line of therapy; anaplastic large cell lymphoma (ALCL) and natural killer T-cell lymphoma nasal type (NKTCL) are excluded\r\n** Advanced stage cutaneous T-cell lymphoma (CTCL), specifically CTCL NOS, small/medium T-cell lymphoma (SMTCL) and mycosis fungoides (MF) stage IB, IIA, IIB, III and IV that have relapsed after at least one specific prior therapy (e.g. interferon, photopheresis, denileukin difitox, bexarotene, etc); anaplastic cutaneous large cell lymphoma (ACLCL) and lymphomatoid papulopsis are excluded\r\n** Follicular lymphoma grade , or A that meets the following criteria: \r\n*** Relapsed or refractory to at least lines of therapy AND\r\n*** Relapsed or refractory post autologous cell transplantation (HCT)\r\n* For dose expansion/dose confirmation phase: \r\n** Patients with confirmed diagnosis of peripheral T-cell lymphoma (PTCL) follicular type or angioimmunoblastic T-cell lymphoma (AITL) that is refractory to at least one line of therapy All cancer diagnoses, except lymphoma, will be eligible Diagnosis of lymphoma Patients with stage I-IV indolent B cell lymphoma, including mucosa-associated lymphoid tissue (MALT) and follicular grade I/II; patients with mantle cell lymphoma will also be included in this study, as mantle cell lymphoma is also radiosensitive, despite it not being an indolent B cell lymphoma; patients with chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL) are ineligible Patients must have a histologically confirmed diagnosis of lymphoma expressing the CD antigen and generally must have failed at least one prior standard systemic therapy; the exception will be mantle cell lymphoma (MCL) patients, who may be enrolled while in first complete remission (CR) as well as other select high-risk lymphomas (e.g., Burkitts, double hit diffuse large B-cell lymphoma [DLBCL], transformed indolent B-cell non-Hodgkin lymphoma [B-NHL], etc.) in accordance with current transplant standard of care for these patients Patients must have newly diagnosed, previously untreated diffuse large B-cell lymphoma, mantle cell lymphoma, grade B follicular lymphoma, Burkitt lymphoma, peripheral T cell lymphoma not otherwise specified (NOS), natural killer (NK)/T cell lymphoma, or transformed lymphoma Natural killer (NK) cell neoplasms\r\n* First complete remission (CR) for patients with high risk natural killer cell neoplasms including myeloid/NK cell precursor acute leukemia, blastic NK-cell lymphoma, aggressive NK-cell leukemia and nasal-type extranodal NK-cell lymphoma in first complete remission\r\n* Second or greater CR Patients with a pathologically confirmed diagnosis of systemic mature T-cell non-Hodgkin lymphoma (NHL) with City of Hope pathology review as per World Health Organization (WHO) classification of lymphomas , who are deemed eligible for high dose therapy and AHCT including patients in:\r\n* T-NHL histologies including peripheral T-cell lymphomas (PTCLs), cutaneous T-cell lymphomas (CTCLs) and natural killer (NK)/T cell lymphomas\r\n** First remission after initial first-line therapy (CR) in PTCL patients, except for anaplastic lymphoma receptor tyrosine kinase (ALK)+ anaplastic large cell lymphoma (ALCL) and CTCL; patients with minimal residual disease after induction therapy may also be eligible at the discretion of the principal investigator (PI)\r\n** Relapsed/refractory disease, stable disease, partial remission (PR) or complete remission (CR), who have received at least lines of therapy, and do not have an adequate allogenetic stem cell transplant option Patients must have a diagnosis of one of the following B-NHL malignancies: chronic lymphocytic leukemia (CLL)/ small lymphocytic lymphoma (SLL), follicular lymphoma (FL), mantle cell lymphoma (MCL), marginal zone lymphoma (MZL), or Waldenstrom macroglobulinemia (WM)/ lymphoplasmacytic lymphoma (LPL); patients with mucosa associated lymphoid tissue (MALT) subtype of MZL may have relapsed or refractory disease after a course of antibiotic therapy; otherwise, patients will not have received standard systemic treatment for their B-NHL before the time of study enrollment; standard systemic therapy is defined by including any of the following agents, representing a comprehensive list of recommended front-line agents used in the treatment of B-NHL: cytotoxic chemotherapies (bendamustine, cyclophosphamide, doxorubicin, vincristine, chlorambucil, cytarabine, gemcitabine, platinum drugs, etoposide); anti-CD antibodies (obinutuzumab, ofatumumab, rituximab); lenalidomide; ibritumomab tiuxetan; proteasome inhibitors (bortezomib, carfilzomib); tyrosine kinase inhibitors (ibrutinib, acalabrutinib, idelalisib); alemtuzumab; corticosteroids unless given for an indication other than treating the B-NHL; or other therapy as determined by the principal investigator (PI)\r\n* Disease: CLL/SLL; Criteria for diagnosis: histopathologic or flow cytometric confirmation\r\n* Disease: FL; Criteria for diagnosis: histopathologic confirmation\r\n* Disease: MZL; Criteria for diagnosis: histopathologic confirmation\r\n* Disease: MCL; Criteria for diagnosis: histopathologic confirmation\r\n* Disease: WM/LPL; Criteria for diagnosis: Per World Health Organization (WHO) criteria STEP : Within days of study entry: T cell leukemia or lymphoma COH pathology review confirms that research participants diagnostic material is consistent with recurrent/progressive/residual B cell lymphoproliferative neoplasms as listed below AND the research participant is not eligible for or declines COH IRB Protocol No. ; additionally, CD positivity must be documented in a pathology report if the research participant previously received CD-targeted therapy; however, it is not a requirement that the CD testing be performed by a COH pathologist\r\n* Disease stratum (NHL): Unclassifiable high grade lymphoma, mantle cell lymphoma, follicular lymphoma, diffuse large B-cell lymphoma (DLBCL) and all its subtypes, Burkitt lymphoma (BL), marginal zone B-cell lymphoma, hairy cell leukemia, lymphoplasmacytic lymphoma, B cell lymphoma unclassifiable with features intermediate between DLBCL and BL, B cell lymphoma unclassifiable with features intermediate between DLBCL and classical Hodgkin lymphoma, and those research participants who either declined or were not eligible for COH IRB Protocol No. , or who collected autologous T cells for COH IRB Protocol No. but then became ineligible for autologous hematopoietic stem cell transplant (HSCT) or participants who have relapsed following prior T cell therapy on either COH IRB Protocol No. or may be enrolled on this study\r\n* Disease stratum (CLL/PLL/SLL): chronic lymphocytic leukemia (CLL), and B-cell prolymphocytic leukemia (PLL), and small lymphocytic lymphoma (SLL) Patients must have histologic or cytologic diagnosis of hematologic malignancies with an indication for allogeneic hematopoietic progenitor cell transplantation, who are ineligible to receive a full ablative conditioning regimen as part of their transplantation, including:\r\n* Acute myeloid leukemia (AML)\r\n** As post-remission therapy in patients with intermediate and high risk cytogenetic and molecular abnormalities, including therapy-related leukemia\r\n** Patients refractory to induction chemotherapy\r\n** Relapsed after complete remission\r\n* Acute lymphocytic leukemia (ALL)\r\n** As post remission therapy in Philadelphia chromosome positive (Ph+) and Philadelphia chromosome negative (Ph-) ALL in complete remission, with or without minimal residual disease in patients older than years of age and those younger than years but ineligible for treatment with fully ablative conditioning regimens\r\n** Relapsed or refractory after prior therapy\r\n* Non Hodgkin lymphoma\r\n** Aggressive lymphoma (Burkitt, diffuse large B cell lymphoma, plasmablastic lymphoma, mantle cell lymphoma) relapsed after autologous hematopoietic progenitor transplantation or patients ineligible to receive autologous hematopoietic progenitor transplantation because of mobilization failure or persistent bone marrow involvement by lymphoma\r\n** Indolent lymphoma (follicular, marginal zone lymphoma, mantle cell lymphoma, etc.) patients are eligible if they have received at least two lines of therapy and have remission of their extramedullary disease\r\n** Indolent and aggressive lymphoma patients with refractory disease to at least two lines of therapy\r\n* Hodgkin lymphoma\r\n** Patients relapsed after autologous hematopoietic progenitor transplantation with remission of at least their extramedullary disease after salvage therapy\r\n** Patients with refractory disease to at least lines of chemotherapy\r\n* Multiple myeloma\r\n** Patients who have presented with relapsed or refractory disease after second line therapy\r\n* Myelodysplastic syndrome\r\n** Patients with International Prognostic Score System Risk rating of: intermediate and higher, ineligible to receive a fully ablative conditioning regimen for allogeneic hematopoietic progenitor cell transplantation\r\n* Chronic lymphocytic leukemia\r\n** Patients with disease relapsed or refractory after or more lines of therapy, ineligible to receive fully ablative conditioning regimens for allogeneic hematopoietic progenitor cell transplantation\r\n** Patients with disease transformed to aggressive lymphoma (Richter transformation) who have received induction therapy for their aggressive disease\r\n* Chronic myeloid leukemia:\r\n** In chronic phase that has failed therapy with at least different tyrosine kinase inhibitors or has progressed to accelerated or blast phase\r\n** In accelerated or blast crisis\r\n* Myeloproliferative syndromes including myelofibrosis\r\n* Complete remission is not necessary for enrollment in this protocol, however Hodgkin and non Hodgkin lymphoma must have had remission of all extramedullary disease to be eligible to participate in this trial Patients must have a previously documented histologic diagnosis of multiple myeloma (MM) Hodgkins Disease (HD) or non-Hodgkins lymphoma (NHL), and be eligible to undergo autologous PBSC transplantation on institutional protocols\r\n* Multiple myeloma should be in first or second partial response or better, as defined by International Myeloma Working Group criteria\r\n* Hodgkins Disease should be primary refractory or relapsed (either chemosensitive or refractory)\r\n* Non-Hodgkins lymphoma must be in either first or second partial response or better and have any one of the following histologies:\r\n** Diffuse large B cell lymphoma\r\n** Transformed lymphoma\r\n** Mantle cell lymphoma\r\n** Follicular lymphoma (any grade)\r\n** Peripheral T cell lymphoma Patients will be ineligible if they have a lymphoma diagnosis Autologous patients can be included anytime within months post-transplant, if they had no signs of progression and meet one of the following criteria: i. leukemia; ii. lymphoma (all types of B and T cell lymphoma); iii. multiple myeloma Diagnosis of recurrent aggressive or indolent B-cell lymphoma or CLL, or newly diagnosed patients unable to receive or complete standard therapy OR diagnosis of relapsed/refractory aggressive B-cell lymphoma with a treatment plan that will include high dose therapy and autologous stem cell transplantation Patients with histologically confirmed B-cell NHL including marginal zone lymphoma, follicular lymphoma, or mantle cell lymphoma by WHO criteria. No prior treatment for mantle cell lymphoma with the exception of corticosteroids for days or less, or course of involved-field radiation Patients with primary tumors including germ cell tumor, or lymphoma/leukemia Pathologically confirmed T-cell lymphomas at the enrolling institution, including stage >= Ib cutaneous T-cell lymphoma (CTCL), which has relapsed or progressed after at least one systemic therapy Receiving systemic therapy for another primary malignancy (other than T-cell lymphoma);\r\n* Patients with more than one type of lymphoma may be enrolled after discussion with the MSK principal investigator\r\n* Adjuvant or maintenance therapy to reduce the risk of recurrence of other malignancy (other than T-cell lymphoma) is permissible after discussion with the MSK principal investigator The following histologies will need to be confirmed at Memorial Sloan-Kettering Cancer Center (MSK) or locally for participating sites in order to be considered for HDT-ASCT and post-transplant maintenance romidepsin:\r\n* Peripheral T-cell lymphoma (PTCL)\r\n* Angioimmunoblastic T-cell lymphoma (AITL)\r\n* Anaplastic large-cell lymphoma (ALCL)\r\n* Enteropathy-associated T-cell lymphoma (EaTCL)\r\n* Hepatosplenic gamma delta T-cell lymphoma\r\n* Adult T-cell leukemia/lymphoma\r\n* Primary cutaneous gamma/delta T-cell lymphoma\r\n* Extranodal natural killer (NK)/T-cell lymphoma, nasal type\r\n* Primary cutaneous anaplastic large cell lymphoma\r\n* Subcutaneous panniculitis-like T-cell lymphoma\r\n* Mycosis fungoides/Sezary syndrome Aggressive non-Hodgkin lymphoma as follows, provided there is stable disease or better to last therapy:\r\n* Natural killer (NK) or NK-T cell lymphoma, peripheral T-cell lymphoma (including angioimmunoblastic T-cell lymphoma, hepatosplenic T-cell lymphoma, subcutaneous panniculitic T-cell lymphoma, and other variants), T-cell prolymphocytic leukemia, or blastic/blastoid variant of mantle cell lymphoma; or\r\n* Hodgkin or aggressive non-Hodgkin lymphoma that has failed at least one multiagent regimen, and the patient is either ineligible for autologous BMT or autologous BMT is not recommended; eligible subtypes of aggressive non-Hodgkin lymphoma include: mantle cell lymphoma; follicular grade lymphoma; diffuse large B-cell lymphoma or its subtypes, excluding primary central nervous system (CNS) lymphoma; primary mediastinal large B-cell lymphoma; large B-cell lymphoma, unspecified; anaplastic large cell lymphoma, excluding skin-only disease; Burkitts lymphoma or atypical Burkitts lymphoma (high-grade B-cell lymphoma, unclassifiable, with features intermediate between diffuse large B-cell lymphoma and Burkitts), in complete remission Follicular lymphoma, marginal zone B-cell lymphoma, lymphoplasmacytic lymphoma, mantle-cell lymphoma, and indolent T-cell lymphomas: Must have progressed with the most recent remission duration being < months; patients with bulky disease should be considered for debulking chemotherapy before transplant; patients with refractory disease are eligible, unless they have bulky disease and an estimated tumor doubling time of less than one month Lymphoma\r\n* Relapsed lymphoma with residual disease that appears to be chemo-sensitive and non-bulky (< cm at largest diameter) Lymphoplasmacytic lymphoma, mantle-cell lymphoma, prolymphocytic leukemia are eligible after initial therapy in CR+ or PR+ Lymphoplasmacytic lymphoma, mantle-cell lymphoma, prolymphocytic leukemia are eligible after initial therapy if chemotherapy sensitive Large cell lymphoma, mantle cell lymphoma and Hodgkin disease that is progressive on salvage therapy; stable disease is acceptable to move forward provided it is non-bulky Any stage for mediastinal gray zone lymphoma (MGZL) and primary mediastinal B cell lymphoma (PMBL) Absolute neutrophil count (ANC) > unless impairment is due to lymphoma or immune-mediated mechanism caused by lymphoma Platelets > , unless impairment is due to lymphoma or immune-mediated mechanism caused by lymphoma Lymphoplasmacytic lymphoma, mantle-cell lymphoma, prolymphocytic leukemia are eligible after initial therapy in CR+ or first partial remission (PR+) Large cell lymphoma, mantle cell lymphoma and Hodgkin disease that is progressing on salvage therapy Any high grade B-cell lymphoma Histologically confirmed peripheral T-cell lymphoma (PTCL) as defined by the World Health Organization (WHO) criteria , excluding cutaneous T-cell lymphoma (CTCL); transformed mycosis fungoides is allowed Patients with B-cell lymphoma who are candidates to autologous stem-cell transplantation, including: . Primary refractory or relapsed diffuse large B-cell lymphoma in response to salvage treatment. . Primary refractory or relapsed follicular lymphoma or other indolent B-cell histology in response to salvage treatment. . Chemosensitive mantle-cell lymphoma in first or later line of treatment. . Patients with B cell lymphoma (all CD+ NHL) with progressive or refractory disease who would otherwise not be candidates for autologous stem cell transplantation Dose escalation cohort:\r\n* Histologically or flow cytometry confirmed diagnosis of B-CLL/small lymphocytic lymphoma (SLL) according to National Cancer Institutesponsored Working Group (NCI-WG) guidelines\r\n* The following types of NHL as documented by medical records and with histology based on criteria established by the World Health Organization (WHO):\r\n** Mantle cell lymphoma (MCL)\r\n** Follicular lymphoma (FL) - grades -a\r\n** Lymphoplasmacytic lymphoma (LPL)\r\n** Marginal zone lymphoma (MZL)\r\n** CLL in Richters transformation\r\n** B-cell prolymphocytic leukemia (B-PLL)\r\n** Diffuse large B-cell lymphoma (DLBCL) Patients must have a histologically documented (either primary or metastatic site) diagnosis of advanced solid tumor cancer (stage IV or unresectable) or aggressive lymphoma (diffuse large B cell lymphoma, mantle cell lymphoma, T cell lymphoma, and natural killer [NK] cell lymphoma)\r\n* NOTE: The following histologies will be excluded: non-small cell lung cancer, squamous cell carcinoma of head and neck, melanoma, renal cell carcinoma, bladder cancer, Hodgkins lymphoma, Merkel cell carcinoma, and high-frequency microsatellite instability (MSI-H) colorectal cancer\r\n* NOTE: Patients with deleterious BRCA / mutated ovarian cancer will be excluded Have a histologically or cytologically confirmed relapsed/refractory mature T-cell lymphoma that has progressed after a minimum of systemic therapy with any of the following T-cell histologies: peripheral T-cell non-Hodgkin lymphoma (NHL), not otherwise specified (PTCL, NOS); anaplastic large cell T-cell lymphoma (ALCL) anaplastic lymphoma kinase positive or negative; angioimmunoblastic T-cell lymphoma; subcutaneous panniculitis like T-cell lymphoma; primary cutaneous gamma-delta T cell lymphoma; enteropathy associated T-cell lymphoma; hepatosplenic T-cell lymphoma; extranodal NK/T-cell lymphoma, nasal type; adult T-cell leukemia/lymphoma; unclassifiable PTCL; and transformed cutaneous T-cell lymphoma (CTCL) to PTCL with systemic involvement (not local skin transformation) Subjects must have histologically confirmed relapsed or refractory non-Hodgkin lymphoma that is not a candidate for standard curative therapy; non-Hodgkin lymphoma (NHL) subtypes include: diffuse large B-cell lymphoma (DLBCL), mantle cell lymphoma, marginal zone lymphoma, lymphoplasmacytic lymphoma, plasmablastic lymphomas, peripheral T-cell lymphomas, and follicular lymphoma of any grade; cutaneous T-cell and B-cell lymphomas will also be eligible in the dose-escalation phase only Biopsy proven NHL, including plasmablastic lymphoma and primary effusion lymphoma but not T-cell lymphoma; tissue histology will be reviewed at City of Hope (COH); patients who have been in remission for >= year post Hodgkin's lymphoma chemotherapy are also considered eligible Prior chemotherapy for lymphoma Biopsy proven lymphoma for which rituximab, etoposide, prednisone, vincristine sulfate, cyclophosphamide, and doxorubicin hydrochloride (R-EPOCH) is appropriate frontline therapy, e.g., Burkitt lymphoma or diffuse large B-cell lymphoma (DLBCL) NHL, including plasmablastic lymphoma and primary effusion lymphoma but not T-cell lymphoma; tissue histology will be reviewed at the treating institution Patients must have histologically or cytologically confirmed Hodgkin lymphoma, Burkitts lymphoma, double-hit lymphoma, other c-Myc positive B-cell lymphoma, diffuse large-B cell lymphoma including those patients with history of transformed follicular lymphoma, mantle cell lymphoma, or peripheral T-cell lymphoma Patient with newly diagnosed, histologically confirmed, group B or C Burkitt lymphoma or leukemia (acute lymphoblastic leukemia, L subtype); diffuse large B-cell lymphoma; or primary mediastinal B-cell lymphoma; patients with group B/C post transplant lymphoproliferative disorder are eligible for the study regardless of whether disease is newly diagnosed B-cell non-Hodgkin lymphoma involving the brain, as demonstrated by contrast-enhanced magnetic resonance imaging (MRI) and histologic confirmation by one of the following within weeks prior to registration: \r\n* A positive cerebral spinal fluid (CSF) cytology for lymphoma or a monoclonal lymphocyte population as defined by cell surface markers\r\n* A biopsy of the vitreous or uvea demonstrating non-Hodgkin lymphoma\r\n* Brain biopsy \r\n* NOTE: patients in whom the type of lymphoma could not be determined or is unknown (e.g., not enough tissue for further analysis) are assumed to have a B-cell lymphoma and are eligible Participants with histologically or cytologically documented diffuse large B-cell lymphoma (DLBCL) must meet at least of the following risk criteria:\r\n* Age-adjusted International Prognostic Index (IPI) score: - \r\n* Ki- >= %\r\n* Histologically, or cytologically documented activated B-cell-like (ABC, also known as post-GCB) subtype \r\n* Double hit variant, defined as having v-myc avian myelocytomatosis viral oncogene homolog (MYC) gene rearrangement in the presence of B-cell chronic lymphocytic leukemia (CLL)/lymphoma (BCL) or BCL gene rearrangement \r\n** Other aggressive non-DLBCL non-Burkitt non-Hodgkin B-cell lymphoma variants as defined by the World Health Organization (WHO) classification, including rare CD negative B-cell lymphomas (i.e. plasmablastic lymphoma, and primary effusion lymphoma) are also eligible; grade B follicular lymphoma is also eligible as long as one the above risk criteria is met Diagnosis of non-Hodgkins lymphoma, transformed B-cell lymphoma, follicular lymphoma, mantle cell lymphoma, diffuse large B-cell or T-cell lymphoma, and deemed a candidate for autologous transplant Recurrent B cell lymphoma or leukemia (ALL or CLL), or newly diagnosed patients unable to receive or complete standard therapy OR diagnosis of relapsed/refractory intermediate B cell lymphoma with a treatment plan that will include high dose therapy and autologous stem cell transplantation; if the patient is less than age , the lymphoma/leukemia is highly aggressive (i.e. lymphoblastic, Burkitt, ALL) Mantle cell lymphoma\r\n* All patients will be eligible in first or greater CR or PR Mature T-cell lymphoma\r\n* T-cell lymphomas including primary T-cell not otherwise specified, angioimmunoblastic, and anaplastic lymphoma kinase (ALK)-positive anaplastic large cell, will be eligible after initial therapy, whether or not CR is achieved\r\n* Mycosis fungoides/Sezary syndrome will be eligible in >= CR/PR Phase subjects with known lymphoma: >= cells/mm (> cell/mm for subjects with lymphoma in bone marrow) T-cell lymphoma Has histologically confirmed diffuse large B-cell lymphoma (DLBCL), primary mediastinal B-cell lymphoma (PMBCL), marginal zone lymphoma (MZL), mantle cell lymphoma (MCL) or histologically and/or cytologically confirmed advanced or metastatic solid tumor and have relapsed or refractory disease following at least two lines of prior standard therapy, including alkylator/anthracycline (unless anthracycline-based chemotherapy is contraindicated)/anti-CD-based therapy (R-CHOP; rituximab, doxorubicin, cyclophosphamide, vincristine, and prednisolone or prednisone, or equivalent) AND must be considered unable to benefit from intensification treatment with autologous hematopoietic stem cell transplantation (ASCT), as defined by meeting at least one of the following criteria: Previous history of treated indolent lymphoma Fluorodeoxyglucose-avid lymphoma (i.e., PET-positive lymphoma) Primary mediastinal B-cell lymphoma Known active cerebral/meningeal lymphoma Previously untreated, histologically confirmed indolent lymphoma including follicle cell lymphoma, World Health Organization (WHO) classification, grade I or II, and marginal zone lymphoma; bone marrow biopsies as the sole means of diagnosis are not acceptable, but they may be submitted in conjunction with nodal biopsies; fine needle aspirates are not acceptable Any prior treatment for non-Hodgkins lymphoma Fluorodeoxyglucose-avid lymphoma Patients who have undergone high-dose therapy and autologous PBSCT for treatment of CD+; NOTE: Based on historical experience of the Indiana University (IU) Bone Marrow and Stem Cell Transplantation Program, it is expected that the vast majority of patients will have been transplanted for diffuse large B-cell lymphoma (DLBCL), follicular lymphoma, or mantle cell lymphoma; however, any patient transplanted for CD+ lymphoma will be considered potentially eligible Pathologically confirmed T or NK cell lymphoma at the enrolling institution; for cutaneous T-cell non-Hodgkin lymphoma (CTCL), patients with stage IB disease or greater are eligible Previous systemic anti-cancer therapy for T-cell lymphoma must have been discontinued at least weeks prior to treatment;\r\n* Glucocorticoids aimed at controlling lymphoma-related symptoms are allowed as long as they are tapered down to mg or less by the time of ruxolitinib initiation\r\n* Topical steroids for CTCL are permitted Platelets >= x ^/L or >= x ^/L (if related to lymphoma) Receiving systemic therapy for another primary malignancy (other than T-cell lymphoma)\r\n* Patients with more than one type of lymphoma may be enrolled after discussion with the Memorial Sloan-Kettering (MSK) principal investigator\r\n* Adjuvant or maintenance therapy to reduce the risk of recurrence of other malignancy (other than T-cell lymphoma) is permissible after discussion with the MSK principal investigator Histologically confirmed diagnosis with review of the diagnostic pathology specimen at one of the participating institutions; eligible histologies are:\r\n* For Arm A: diffuse large B cell lymphoma; patients with a prior history of indolent B-cell non-Hodgkin lymphoma (NHL) are eligible, as long as they have histologically confirmed diffuse large B cell lymphoma (DLBCL) prior to their pretransplant salvage treatment; patients with mediastinal large B cell lymphoma are also eligible\r\n* For Arm B: classical Hodgkin lymphoma (patients with nodular lymphocyte predominant Hodgkin lymphoma [NLPHL] are NOT eligible)\r\nFor Arm C: peripheral T cell lymphoma eligible subtypes will include peripheral T-cell lymphoma (PTCL), not otherwise specified (NOS); angioimmunoblastic T cell lymphoma (AITL); ALK-negative anaplastic large cell lymphoma (ALCL); enteropathy-associated T-cell lymphoma (EATL) and monomorphic epitheliotropic intestinal T-cell lymphoma (MEITL); and extranodal NK/T-cell lymphoma (ENKTL); patients with other PTCL histologies, including ALK-positive PTCL, and cutaneous T-cell lymphoma will not be eligible No prior anti-lymphoma treatment. Composite lymphoma or transformed lymphoma. Patient has histologically confirmed diagnosis of R/R mantle cell lymphoma, follicular lymphoma or diffuse large B cell lymphoma\r\n* Diffuse large B cell lymphoma patients has received at least prior regimen and received, declined, or is ineligible for autologous or allogeneic stem cell transplant\r\n* Follicular lymphoma patients have received at least lines of therapy\r\n* Mantle cell lymphoma patients has received at least line of therapy\r\n* Allogeneic stem cell transplant recipients be greater than months post transplant, not on immunosuppression for prevention of graft versus host disease for > months and without active graft versus host disease are eligible\r\n* Autologous stem cell transplant recipients must have adequate bone marrow recovery and transfusion independent\r\n* Transformed histologies are permitted Histologically documented CD-positive lymphoma and fluorodeoxyglucose (FDG)-avid lymphoma (that is PET-positive lymphoma) with at least one bi-dimensionally measurable lesion Any previous chemotherapy or radiation for mantle cell lymphoma; short course of steroids for symptom relief prior to presentation is permissible Histologically confirmed new diagnosis of stage II, III and IV peripheral T-cell non-Hodgkins lymphoma not otherwise specified (NOS), anaplastic large cell lymphoma (ALK negative) (ALK positive if IPI , , or ), angioimmunoblastic T-cell lymphoma, enteropathy associated T-cell lymphoma, hepatosplenic gamma delta T-cell lymphoma Patients with a diagnosis of other peripheral T-cell lymphoma (PTCL) histologies other than those specified in the inclusion criteria Have had no prior systemic treatment for lymphoma Pathologically confirmed B- or T-cell lymphomas at the enrolling institution, including stage >= Ib cutaneous T-cell lymphoma (CTCL), which has relapsed or progressed after at least one systemic therapy\r\n* Hodgkin lymphoma is allowed and will be classified as a B-cell lymphoma in the phase IIA portion Patients must have a confirmed diagnosis of mantle cell lymphoma with positivity in tissue biopsy Disease status: all the patients need to have scan or biopsy proven active disease at the time of clinical trial\r\n* Multiple myeloma: patient must have failed at least one line of therapy\r\n* Chronic lymphocytic leukemia (CLL): status post (S/P) at least one line of therapy\r\n* Hodgkins lymphoma: S/P at least two lines of therapy\r\n* Follicular lymphoma: S/P at least one line of therapy\r\n* Mantle cell lymphoma: S/P at least one line of therapy\r\n* Diffuse large B cell lymphoma: S/P at least two lines of therapy All patients must have a pathologic diagnosis of one of the following malignancies:\r\n* Non-Hodgkins lymphoma, including B- and T-cell lymphoma\r\n* Multiple myeloma or another plasma cell dyscrasia (Waldenstrom, Amyloidosis) Patients must have histologically confirmed B-cell NHL; acceptable subtypes of B-cell NHL include follicular lymphoma (grades , , or a), marginal zone lymphoma, or lymphoplasmacytic lymphoma/Waldenstroms macroglobulinemia; patients with mantle cell lymphoma must have a documented t(;) or overexpression of cyclin D by immunohistochemical evaluation; patients with diffuse large B cell lymphoma must have activated B cell subtype as defined by the Hans criteria; however, patients with a history of large cell transformation are eligible provided that there is no current clinical evidence of active transformed lymphoma Histologically confirmed mantle cell lymphoma (MCL) Relapse or progression after at least one systemic therapy for mantle cell lymphoma Diagnosis of lymphoma Prior history of indolent lymphoma Patients with aggressive B-cell non-Hodgkin lymphoma subtypes including, relapsed or refractory diffused large B-cell lymphoma (DLBCL) and transformed follicular lymphoma meeting at least one of the following criteria:\r\n* Bone marrow involvement at the time of relapse or refractory disease and not appropriate for allogeneic transplantation\r\n* Positron emission tomography (PET) positive disease outside of one radiation port, unless single-port disease treated with prior radiotherapy within the port, following >= cycles of salvage chemotherapy, per International Working Group (IWG) criteria Diagnosis of islet cell tumor, lymphoma, metastatic lesion, acinar cell (or other atypical pathologic malignancy) Pathology confirmed lymphoma or multiple myeloma\r\n* Hodgkin lymphoma is eligible for either phase and will be considered a B-cell lymphoma in the phase IIa study\r\n* Phase IIa portion, subjects must have B-cell lymphoma, T-cell lymphoma, or multiple myeloma Participants must have histologically confirmed Hodgkin lymphoma or non-Hodgkin lymphoma, (including, but not limited to, diffuse large B-cell lymphoma [DLBCL] or primary mediastinal B-cell lymphoma [PMBCL], Ann Arbor stage I-II disease, or stage III-IV disease with a dominant presenting mass within the mediastinum); pathology must be reviewed and confirmed at Massachusetts General Hospital (MGH) or other Dana-Farber (DF)/Harvard Cancer Center (HCC) institution Indolent B-cell NHL lymphoma (study part B): No prior radiation therapy for mantle cell lymphoma Patients with the following cluster of differentiation (CD)+ lymphoid malignancies who are eligible for allogeneic transplantation:\r\n* Relapsed or refractory follicular lymphoma\r\n* Relapsed or refractory or high risk mantle cell lymphoma (hi ki; blastic)\r\n* Recurrent or refractory marginal zone\r\n* Recurrent or refractory chronic lymphocytic leukemia (CLL)/small lymphocytic lymphoma\r\n* Double-hit lymphoma\r\n* Diffuse large B cell lymphoma\r\n* Richter's patients\r\n* Refractory or recurrent Burkitts Have no prior systemic treatment for lymphoma Patients with histologically confirmed aggressive B-cell lymphoid malignancy, such as diffuse large B cell lymphoma (DLBCL), including primary mediastinal large B cell lymphoma, T cell rich B cell lymphoma, \double hit\ DLBCL, mantle cell lymphoma, any transformed low grade B cell lymphomas or grade follicular lymphoma (grade a or b) who were refractory to rituximab-cyclophosphamide-hydroxydaunorubicin (doxorubicin hydrochloride)-Oncovin (vincristine sulfate)-prednisone (R-CHOP)-like or any anthracycline based chemotherapy or relapsed after at least one prior combination chemotherapeutic regimen and who are deemed candidates for a salvage type chemotherapy\r\n* Relapsed disease:\r\n**Progressive disease after a CR for at least days; progression will be defined according to the Revised Response Criteria for Malignant Lymphoma (Cheson )\r\n* Refractory disease:\r\n**Subjects must meet one of the following criteria:\r\n*** Persistent or progressive lymphoma with a CR of < days duration or with a PR of any duration; subjects must have received at least cycles of RCHOP-like or any anthracycline base chemotherapy or at least full cycles of hyperfractionated cyclophosphamide-vincristine sulfate-Adriamycin (doxorubicin hydrochloride)-dexamethasone (HyperCVAD)-like chemotherapy\r\n*** Persistent lymphoma and stable disease after at least cycles of RCHOP-like or any anthracycline base chemotherapy or at least full cycle of HyperCVAD-like chemotherapy (part A and B)\r\n*** Progressive disease despite at least cycle of RCHOP-like or any anthracycline base chemotherapy or at least cycle (part A or A and B) of HyperCVAD-like chemotherapy Primary germ cell tumor, small cell carcinoma, or lymphoma The following disease types are eligible: transformed lymphomas: diffuse large B cell lymphoma, mantle cell lymphoma, follicular lymphoma grade III; precursor B lymphoblastic leukemia/lymphoma; mediastinal (thymic) large B-cell lymphoma; Burkitt lymphoma/leukemia; precursor T-lymphoblastic leukemia/lymphoma; primary cutaneous anaplastic large cell lymphoma; anaplastic large cell lymphoma primary systemic type; small lymphocytic lymphoma/chronic lymphocytic leukemia; follicular lymphoma, grades , ; extranodal marginal zone B-cell lymphoma of mucosa-associated lymphatic tissue (MALT) type; nodal marginal zone B-cell lymphoma; splenic marginal zone B-cell lymphoma; peripheral T cell lymphoma, unspecified; anaplastic large cell lymphoma (T and null cell type); lymphoplasmacytic lymphoma (Waldenstrom Macroglobulinemia); CNS lymphoma; post transplant lymphoproliferative disorders; mycosis fungoides/Sezary syndrome; primary effusion lymphoma; blastic natural killer (NK)-cell lymphoma; adult T-cell leukemia/lymphoma; extranodal NK/T-cell lymphoma, nasal type; enteropathy-type T-cell lymphoma; hepatosplenic T-cell lymphoma; subcutaneous panniculitis-like T-cell lymphoma; angioimmunoblastic T-cell lymphoma; anaplastic large cell lymphoma primary cutaneous type; T-cell prolymphocytic lymphoma Have confirmed mantle cell lymphoma diagnosis. Patients must have one of the following relapsed/ refractory lymphoid malignancies: chronic lymphocytic leukemia (CLL), small lymphocytic lymphoma (SLL) or B-prolymphocytic leukemia which has been previously treated with a purine analog, and are not candidates for higher priority clinical studies; follicular lymphoma, mantle cell lymphoma, lymphoplasmacytoid lymphoma or marginal zone lymphoma which has been previously treated with autologous or allogeneic stem cell transplantation; T-cell prolymphocytic leukemia, large granular lymphocyte leukemia, mycosis fungoides / Sezary syndrome or peripheral T-cell lymphoma which has been previously treated with at least one line of chemotherapy or monoclonal antibody therapy; T-cell or B-cell acute lymphoblastic leukemia (ALL) which has been previously treated with at least one line of chemotherapy Persistent, or relapsed non-Hodgkin's lymphoma (NHL) (any histology) that is chemo-resistant (< a partial response [PR]), subjects who have received >= prior chemotherapy regimens, or subjects with lymphomas that have a high relapse rate following autologous or syngeneic stem cell transplantation (transformed NHL, peripheral T-cell lymphoma [PTCL], mantle cell lymphoma, anaplastic lymphoma kinase [ALK]-negative anaplastic large cell lymphoma [ALCL, alk neg]), intermediate International Prognostic Index (IPI) or high risk IPI or subjects with a positive positron emission tomography (PET) scan prior to transplant, and otherwise eligible for transplantation with adequate end-organ function Chemosensitive NHL, except subjects receiving >= prior chemotherapy regimens, or subjects having transformed NHL, PTCL, mantle cell lymphoma (MCL) or ALCL, alk neg NK cell neoplasms\r\n* First complete remission (CR) for patients with high risk natural killer cell neoplasms including myeloid/NK cell precursor acute leukemia, blastic NK-cell lymphoma, aggressive NK-cell leukemia and nasal-type extranodal NK-cell lymphoma in first complete remission\r\n* Primary induction failure\r\n* Second or greater CR T-cell neoplasm: adult T-cell leukemia/lymphoma, hepatosplenic T-cell lymphoma, and enteropathy associated T-cell lymphoma\r\n* First CR\r\n* Chemotherapy-refractory disease\r\n* Relapse after greater than or equal to prior regimen For patient with NK cell neoplasms: ) patients with high risk natural killer cell neoplasms including myeloid/NK cell precursor acute leukemia, blastic NK-cell lymphoma, aggressive NK-cell leukemia and nasal-type extranodal NK-cell lymphoma in first complete remission; ) all NK cell neoplasms can be transplanted in: a) primary induction failure or b) second or greater complete remission For patients with T-cell neoplasms including adult T-cell leukemia/lymphoma, hepatosplenic T-cell lymphoma and enteropathy associated T-cell lymphoma\r\n* First CR\r\n* Chemotherapy-refractory disease\r\n* Relapse after greater than or equal to prior regimen For patients with non-Hodgkins lymphoma, they must be determined to have at least stable disease to last therapy Lymphoma accessible for sampling or existing cryopreserved lymphoma tumor judged suitable for preparation of vaccine CD detectable B lineage relapsed refractory NHL including the following histologies: \r\n* Aggressive lymphomas: diffuse large B cell lymphoma, primary mediastinal B cell lymphoma, grey zone lymphomas, high grade B cell lymphomas, and transformed indolent lymphomas\r\n* Indolent lymphoma: follicular lymphoma, marginal zone lymphoma, small lymphocytic lymphoma; indolent lymphoma patients eligible for this trial should have high tumor burden and high risk disease, as defined by:\t\r\n** The Groupe dEtude des Lymphomes Folliculaires (GELF) criteria\r\n** Intermediate or high risk by Follicular Lymphoma International Prognostic Index (FLIPI) score or elevated lactose dehydrogenase (LDH)/ beta- microglobulin (BM) Patients with CD positive Hodgkin lymphoma (HL) or anaplastic large cell lymphoma (ALCL) that have undergone allogeneic or haploidentical stem cell transplant (SCT) in the past days (matched related or matched unrelated donors only) Histologically or cytologically documented newly diagnosed (stages II, III or IV) Myc-positive diffuse large B-cell lymphoma (DLBCL), transformed follicular lymphoma, or high-grade unclassifiable with features intermediate between DLBCL and Burkitt lymphoma (per the World Health Organization [WHO] classification of lymphoid neoplasm) OR histologically or cytologically-documented newly diagnosed (stages II, III or IV) DLBCL not otherwise specified (NOS) or high-grade B-cell lymphoma with Myc and B-cell lymphoma (Bcl) and/or B-cell lymphoma (Bcl) (per the revision of the WHO classification of lymphoid neoplasms) Hodgkin's variant of Richter's lymphoma, accelerated CLL, composite lymphoma, interdigitating dendritic cell sarcoma, sarcoma, EBV-associated lymphoma or prolymphocytic transformation. Patients must have histologically proven T-cell lymphoma, including the following subtypes:\r\n* Peripheral T-cell lymphoma, not otherwise specified\r\n* Angioimmunoblastic T-cell lymphoma\r\n* Anaplastic large cell lymphoma, anaplastic lymphoma receptor tyrosine kinase (ALK) positive\r\n* Anaplastic large cell lymphoma, ALK negative\r\n* Mycosis fungoides\r\n* Sezary syndrome T-cell primary CNS lymphoma. Confirmed diagnosis of mantle cell lymphoma Previous history of treated indolent lymphoma T/natural killer (NK)-cell leukemia/lymphoma Anaplastic large cell lymphoma (ALCL), primary systemic type, excluding anaplastic lymphoma kinase positive (ALK+) with International Prognostic Index (IPI) score less than at initial diagnosis and complete response (CR) after CHOP-based therapy Extranodal T/NK-cell lymphoma nasal or nasal type Previously treated CLL or other B-cell neoplasm including small lymphocytic lymphoma, hairy cell leukemia, follicular lymphoma, Waldenstroms macroglobulinemia, marginal zone lymphomas, mantle cell lymphomas, lymphoplasmacytic lymphoma and diffuse large B-cell lymphoma; patients with composite lymphoma and transformed disease will be included; immunophenotypic (or immunohistochemical) analysis of the malignant lymphocytes should demonstrate that the cells are B-cells High grade B-cell lymphoma (HGBCL) Relapsed/refractory Hodgkin lymphoma or NHL patients (e.g. histologies include: any subtype of Hodgkin lymphoma, chronic lymphocytic leukemia (CLL)/small lymphocytic lymphoma (SLL), any subtype of marginal zone, follicular [grades , or ], diffuse large B-cell lymphoma (DLBCL) [including any morphological variants], transformed lymphoma, mantle cell, lymphoplasmacytic lymphoma and peripheral T-cell lymphoma (PTCL) [but excluding cutaneous T-cell, precursor T-cell or B-cell lymphoma, or Burkitt lymphoma]), who have relapsed or are refractory after receiving a minimum of two prior systemic therapies (i.e., excludes patients who have involved field radiation therapy for limited stage disease); patients who have undergone prior autologous (but not allogeneic) stem cell transplantation are eligible for this study as long as they meet all other required inclusion/exclusion criteria Non-Hodgkins Lymphoma subjects that have received at least one prior treatment (Antibodies and / or chemotherapy); subjects must have one of the following subtypes according to the World Health Organization (WHO)/Revised European American Lymphoma (REAL) Classification():\r\n* Follicular lymphoma, diffuse large cell lymphoma, mantle cell lymphoma and small lymphocytic lymphoma / chronic lymphocytic lymphoma Any T cell lymphoma In addition, cutaneous B and T cell lymphoma are permitted; cutaneous T cell lymphoma must be refractory to prior systemic therapy (topical therapy, photophoresis, radiation are not considered systemic therapy); transformed B and T cell cutaneous lymphoma are also permitted Relapsed/refractory nodal, leukemic, and extranodal T cell lymphomas are eligible; subtypes eligible include anaplastic large cell lymphoma, angioimmunoblastic T cell lymphoma, peripheral T-cell lymphoma-not-otherwise specified (PTCL-NOS), nasal or disseminated extranodal T/natural killer (NK) lymphoma, enteropathy-associated T cell lymphoma, hepatosplenic gamma/delta T cell lymphoma, subcutaneous panniculitis-like T cell lymphoma, T-prolymphocytic leukemia, adult T-cell leukemia/lymphoma, large granular lymphocytic leukemia, aggressive NK leukemia Diagnosis of mantle or diffuse large-cell lymphoma, Grade B follicular lymphoma [Harris, Swerdlow et al. ] or gastric mucosa-associated lymphoid tissue (MALT) lymphoma Received any prior therapy for lymphoma Enteropathy-Associated T cell Lymphoma (EATL) Primary disease of hematologic origin, lymphoma, or small cell cancer Patients with non-Hodgkins lymphoma and one or more of the following: \r\n* Diffuse large B-cell lymphoma with one or more of the following: \r\n** Primary refractory disease\r\n** Relapse within months of completion of first-line therapy\r\n** Secondary International Prognostic Index (IPI) > \r\n** Less than partial remission (PR) to first-line salvage chemotherapy\r\n** Kinetic failure after salvage chemotherapy\r\n** Prior treatment with or more lines of therapy\r\n** Patients with double-hit or triple-hit non-Hodgkin lymphoma (NHL), in any state of the disease\r\n* Peripheral T-cell lymphoma not otherwise specified (PTCL-NOS) in any stage of the disease\r\n* Angioimmunoblastic T-cell lymphoma (AITL) in any stage of the disease\r\n* Refractory or recurrent Burkitts lymphoma\r\n* Any other lymphoma that is refractory or relapsed and that does not qualify for treatment protocols of higher priority Participants must have histologically confirmed peripheral T-cell lymphoma, with the diagnostic specimen reviewed at one of the Dana-Farber Harvard Cancer Center (DFHCC) hematopathology laboratories; eligible histologies include:\r\n* PTCL-not otherwise specified (NOS)\r\n* Systemic T cell/null anaplastic large cell lymphoma (ALCL), regardless of anaplastic lymphoma kinase (Alk)-status\r\n* Angioimmunoblastic T-cell lymphoma (AITL)\r\n* Hepatosplenic (alpha-beta or gamma-delta) lymphoma (HSL)\r\n* Enteropathy-associated T-cell lymphoma (EATL)\r\n* Adult T-cell leukemia/lymphoma (ATLL), lymphomatous subtype\r\n* Subcutaneous panniculitis-like T-cell lymphoma\r\n* T-cell prolymphocytic leukemia (T-PLL)\r\n* Natural killer (NK) cell lymphoma/leukemia Patients with extranodal NK T-cell lymphoma Has enlarged lymph node(s) highly suspicious of lymphoma; or has been diagnosed with lymphoma but is untreated; or has persistent recurrent, or progressive lymphoma Patients must have histologically proven relapsed or refractory B-cell NHL of the following World Health Organization (WHO) classification subtypes: follicular lymphoma (FL), mantle cell lymphoma (MCL), lymphoplasmacytic lymphoma/Waldenstrms macroglobulinemia (LPL/WM), marginal zone lymphoma (MZL), diffuse large B-cell lymphoma (DLBCL), Burkitts lymphoma (BL), and B-cell lymphoma with features unclassifiable between Burkitts and large cell lymphoma; alternatively, patients with histologically proven, newly diagnosed transformed non-Hodgkins lymphoma (tNHL) are eligible Prior therapy for lymphoma Relapsed or refractory NHL including tumor types: Follicular lymphoma (FL), marginal zone lymphoma (MZL)/mucosa-associated lymphoid tissue (MALT), diffuse large B-cell lymphoma (DLBCL), mantle cell lymphoma (MCL), chronic lymphocytic leukemia (CLL). Relapsed, refractory, or progressive aggressive non-Hodgkins lymphoma (including mantle cell lymphoma), with partial response (PR) or better prior to transplantation, and autologous BMT is not recommended;\r\n* Note: Patients with Burkitts, atypical Burkitts, or acute lymphoblastic lymphoma must be in complete remission (CR) One of the following poor-risk lymphomas or plasma cell neoplasms, in PR or better prior to transplantation:\r\n* Transformed lymphoma\r\n* T-cell prolymphocytic leukemia (PLL)\r\n* Peripheral T-cell lymphoma\r\n* Natural killer (NK) or NK/T-cell lymphoma\r\n* Blastic/blastoid mantle cell lymphoma\r\n* Plasma cell leukemia Current diagnosis of primary cutaneous anaplastic large cell lymphoma, mycosis fungoides, Sezary syndrome or other primary cutaneous lymphomas; extranodal NK/T-cell lymphoma, nasal type Lymphoplasmacytic lymphoma mantle cell lymphoma Meets one of the following need-for-treatment criteria (with the exception of mantle cell lymphoma for which treatment is indicated): presence of lymphoma-related complications, including narrowing of ureters or bile ducts, tumor-related compression of a vital organ, lymphoma-induced pain, cytopenias related to lymphoma/leukemia, splenomegaly, pleural effusions, or ascites Adequate hematologic function (unless abnormalities related to lymphoma infiltration of the bone marrow or hypersplenism due to lymphoma) as follows: Corticosteroids for treatment of lymphoma within days of study entry Chronically administered low-dose corticosteroids (e.g., prednisone ? mg/day) for indications other than lymphoma or lymphoma-related complications are permitted Patients must be newly diagnosed with mantle cell lymphoma, have an accessible disease site for excisional biopsy or have sufficient peripheral blood tumor to leukapheresis at least . x ^ lymphoma cells in a single session Documentation of diagnosis as evidenced by one or more clinical features consistent with mycosis fungoides cutaneous T-cell lymphoma Aggressive B-cell lymphoma, including DLBCL and follicular lymphoma (FL) or other indolent or low grade malignancy transforming to DLBCL, grade III FL, Burkitt lymphoma, and unclassifiable B-cell lymphoma with features of Burkitt and DLBCL according to the World Health Organization, with biopsy confirmation of disease which has relapsed after or refractory to a standard cytotoxic chemotherapy combination including rituximab and doxorubicin, for whom an autologous stem cell transplant is planned No prior chemotherapy for lymphoma Survivors of mediastinal lymphoma (either non-Hodgkins lymphoma or Hodgkins lymphoma) with no active malignancy Previously untreated mantle cell lymphoma patients (at least clinical stage ) Absolute neutrophil count (ANC) >= , unless felt to be secondary to underlying mantle cell lymphoma Platelet count >= ,, unless felt to be secondary to underlying mantle cell lymphoma Confirmed diagnosis of B-cell Non-Hodgkin's lymphoma limited to follicular lymphoma (FL), diffuse large B-cell lymphoma (DLBCL), mantle cell lymphoma (MCL), marginal zone lymphoma (MZL), primary mediastinal B-cell lymphoma (PMBL), or chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL) that has progressed and for which standard curative measures do not exist or are no longer effective. Prior therapy must have included a rituximab-based regimen. Diagnosis of lymphoma or leukemia as documented in medical record Patients with mantle cell lymphoma (MCL) with stage or disease Lymphoplasmacytic lymphoma, mantle-cell lymphoma, prolymphocytic leukemia are eligible after initial therapy if chemotherapy sensitive Subjects with a diagnosis of lymphoma falling into the following categories:\r\n* Diffuse large B-cell lymphoma (DLBCL) who have received cycle of anthracycline-based chemotherapy\r\n* DLBCL in complete remission and within months after completion of anthracycline-based chemotherapy\r\n* Chronic lymphocytic leukemia (CLL) or mantle cell lymphoma (MCL) receiving ibrutinib for at least month\r\n* Follicular lymphoma (FL) in remission and on surveillance for or more months\r\n* Aggressive peripheral T-cell lymphoma (PTCL) who have received cycle of chemotherapy Patients with aggressive non-Hodgkins lymphoma (NHL), including diffuse large cell lymphoma, mediastinal B-cell lymphoma, transformed lymphoma, mantle cell lymphoma, and peripheral T cell lymphoma, who also have one of the following criteria:\r\n* Failure to achieve complete remission to primary induction therapy\r\n* Relapsed and refractory to at least one line of salvage systemic therapy\r\n* Failed stem cell collection Lymphoplasmacytic lymphoma, mantle-cell lymphoma, prolymphocytic leukemia are eligible after initial therapy if chemotherapy sensitive Large cell lymphoma, mantle cell lymphoma and Hodgkin disease that is progressing on salvage therapy Study - Aggressive lymphoma\r\n* Newly diagnosed de-novo DLBCL or primary mediastinal B-cell lymphoma that will be treated with an anthracycline-containing regimen (rituximab-cyclophosphamide, doxorubicin hydrochloride, prednisone [R-CHOP] or equivalent) \r\n* Patients with composite lymphomas (low grade and large cell; marginal and large cell; nodular lymphocyte predominant [LP] Hodgkin and large cell, etc) at the time of original diagnosis can also be enrolled as long as they have large cell component and will be treated with an anthracycline\r\n* Patients with high-grade B-cell lymphoma with rearrangements of MYC and BCL and/or BCL (formerly DLBCL with double or triple hit), high-grade B-cell lymphoma, not otherwise specified (NOS), B-cell lymphoma, unclassifiable, with features intermediate between DLBCL and classical Hodgkin lymphoma, and post-transplant DLBCL are also eligible as long as they meet other criteria and are receiving RCHOP-based therapy\r\n** NOTE: patients can be enrolled up through day of cycle of therapy; the patient is permitted to participate in any other therapeutic therapy for their disease as long as it does not concern vitamin D; patients can begin their chemotherapy while awaiting vitamin D results and treatment arm assignment or\r\n* Newly diagnosed untreated peripheral T-cell non-Hodgkin lymphoma (NHL) that will be treated with chemotherapy; NOTE: patients can be enrolled up through day of cycle of therapy; this includes the following disease types:\r\n** Peripheral T cell lymphoma, unspecified\r\n** Anaplastic large cell lymphoma (T and null cell type)\r\n** Extranodal NK/T-cell lymphoma, nasal type\r\n** Enteropathy-type T-cell lymphoma\r\n** Hepatosplenic T-cell lymphoma\r\n** Subcutaneous panniculitis-like T-cell lymphoma\r\n** Angioimmunoblastic T-cell lymphoma\r\n** Anaplastic large cell lymphoma primary cutaneous type and\r\n* Willing to provide tissue for correlative research purposes High grade B-cell lymphoma with MYC and BCL and/or BCL rearrangements with DLBCL histology (double/triple-hit lymphoma) History of lymphoma For the Dose Escalation phase, participants must have histologically confirmed diagnosis of advanced NHL of any histology (with the exception of participants with mantle cell lymphoma [MCL] or chronic lymphoma leukemia [CLL]).