Patients must have follicular lymphoma (grade I, II or IIIa) confirmed at initial diagnosis and at relapse with identifiable fludeoxyglucose F- (FDG) avid disease on PET/CT; patients that have involvement with large cell lymphoma are not eligible Histologically confirmed, relapsed or refractory, follicular B-cell NHL (follicular lymphoma) Grade , , and a. Grade b follicular lymphoma DLBCL with mucosa-associated lymphoid tissue (MALT) lymphoma, composite lymphoma (HL+NHL) or DLBCL transformed from diseases other than indolent NHL. One of the following untreated, histological confirmed lymphoma expressing cluster of differentiation (CD) antigen\r\n* DLBCL with disconcordant and/or composite pathology e.g. low grade follicular lymphoma within bone marrow or lymph node are eligible\r\n* DLBCL transformation follicular lymphoma (FL) untreated with anthracyclines or high dose chemotherapy/autologous stem cell transplantation; patients treated with rituximab alone, non-anthracycline containing regiments and previously observed only are eligible Patients must have histologically confirmed transformed diffuse large B-cell lymphoma (DLBCL), including histologic transformation from any indolent lymphoma (e.g. follicular or marginal zone lymphoma); (patients with Richter transformation of chronic lymphocytic leukemia/small lymphocytic lymphoma are excluded) All risk by Follicular Lymphoma International Prognostic Index (FLIPI) - factors Patients must have histologically confirmed diffuse large B-cell lymphoma (DLBCL); patients with previously diagnosed indolent lymphoma (follicular lymphoma and marginal zone lymphoma but not small lymphocytic lymphoma) who have transformed to DLBCL are eligible only if they have not previously been treated for indolent lymphoma; for the Phase II study, patients must have non-GC DLBCL as determined by Hans Algorithm Cohort #: histologically confirmed CD-positive, relapsed or refractory DLBCL, including de novo and transformed DLBCL (from follicular or marginal zone lymphoma); this includes patients with DLBCL who are found to have small cell infiltration of the bone marrow or other diagnostic material (representing a discordant lymphoma) Transformed lymphoma Patients with indolent non-Hodgkin lymphoma (NHL) must have had >= regimen of rituximab-containing regimen; Note: this includes follicular lymphoma (FL), marginal lymphoma and mucosa-associated lymphoid tissue (MALT) Histologically proven DLBCL, including transformation from follicular lymphoma History of follicular lymphoma grade B DLBCL cohort: DLBCL, not otherwise specified (NOS; includes transformed DLBCL from indolent histology [tDLBCL]), high-grade B-cell lymphoma with MYC and BCL and/or BCL rearrangements with DLBCL histology (Swerdlow ), primary mediastinal B-cell lymphoma (PMBCL), and follicular lymphoma Grade B. Subjects must have been treated with an anthracycline and rituximab (or other CD-targeted agent) and have relapsed or refractory disease after at least lines of therapy or after auto-HSCT. Diagnosed with relapsed or refractory de novo DLBCL or follicular lymphoma transformed to DLBCL to one previous line of anthracycline-containing chemotherapy Follicular Lymphoma I, II, IIIA Biopsy-confirmed grade or , or A follicular lymphoma; mantle cell lymphoma; or marginal zone lymphoma; subjects must have relapsed from or are refractory to prior therapy Patients with a low grade lymphoma or CLL and a concurrent high grade lymphoma transformed from the low grade lymphoma or CLL will be eligible Transformation to high-grade lymphoma secondary to previously untreated low-grade lymphoma. Follicular lymphoma G--a Histologically confirmed diagnosis of follicular lymphoma grade b or transformed disease, or chronic lymphocytic leukemia. Previously untreated diffuse large B-cell lymphoma or grade B follicular lymphoma (of any stage); subjects must be planned to receive full course ( cycles) of RCHOP chemoimmunotherapy as per clinical standard of care; patients may have de novo DLBCL, and /or any of the following:\r\n* Composite lymphomas, which include both diffuse DLBCL and another histology (most commonly follicular lymphoma) in the same lymph node\r\n* Transformed lymphoma with DLBCL histology, as long as the patient has not received prior therapy for lymphoma\r\n* Discordant presentations, such as DLBCL in a lymph node and low-grade lymphoma such as follicular lymphoma in the bone marrow Inclusion Criteria:\n\n -- Age ? years\n\n - Histologically confirmed Follicular Lymphoma (Grade , or a), Marginal Zone\n Lymphoma, or Mantle Cell Lymphoma\n\n - Must have documented relapsed, refractory or Progressive Disease after last treatment\n with systemic therapy\n\n - Bi-dimensionally measurable disease\n\n - Eastern Cooperative Oncology Group (ECOG) Performance status ? \n\n - Adequate bone marrow function\n\n - Willingness to follow pregnancy precautions\n\n Exclusion Criteria:\n\n - Histology other than follicular or marginal zone lymphoma or clinical evidence of\n transformation or Grade b follicular lymphoma\n\n - Any medical condition (other than the underlying lymphoma) that requires chronic\n steroid use\n\n - Subjects taking corticosteroids during the last week prior treatment, unless\n administered at a dose equivalent to < mg/day of prednisone\n\n - Systemic anti-lymphoma therapy within days or use of antibody agents within weeks\n use of radioimmunotherapy within months\n\n - Known seropositive for or active viral infection with hepatitis B virus (HBV),\n hepatitis C virus (HCV), human immunodeficiency virus (HIV)\n\n - Known sensitivity or allergy to murine products\n\n - Presence or history of central nervous system involvement by lymphoma. Subjects who\n are at a risk for a thromboembolic event and are not willing to take prophylaxis for\n it.\n\n - Any condition that places the subject at unacceptable risk if he/she were to\n participate in the study or that confounds the ability to interpret data from the\n study. Histologically confirmed diagnosis of follicular lymphoma grade b or transformed disease, or chronic lymphocytic leukemia A diagnosis of small lymphocytic lymphoma, follicular lymphoma (grades -a), or marginal zone lymphoma Biopsy-confirmed low-grade B-cell or cutaneous T cell lymphoma; specifically, follicular grade , , or A, marginal zone or small lymphocytic lymphoma, or mycosis fungoides of any initial stage; patients in cohort A must have had no prior systemic therapy and patients in cohort B must be relapsed/refractory after at least one prior systemic therapy Confirmed diagnosis of low tumour burden, CD+ follicular lymphoma Biopsy proven B-NHL (biopsy proven at least at primary diagnosis), including DLBCL that represents transformation of indolent NHL (including follicular, marginal zone, and lymphoplasmacytic lymphoma excluding chronic lymphocytic leukemia or Hodgkin Lymphoma), FL, and MCL. Presentations of these histologies with substantial occurrence of malignant cells into the bloodstream (lymphocyte count ? x ^/L) including all leukemic presentations are excluded. Subjects with transformation of indolent lymphoma must have received therapy after a diagnosis of transformation that is appropriate for aggressive histology as described in . The following histologies are not eligible: Lymphoblastic lymphoma, Burkitt lymphoma. Any histologies not specifically mentioned must be discussed with the medical monitor. For Part (Expansion in patients with DLBCL): only biopsy proven DLBCL (biopsy proven at least at primary diagnosis), including DLBCL that represents transformation of indolent NHL (including follicular, marginal zone, and lymphoplasmacytic lymphoma excluding chronic lymphocytic leukemia or Hodgkin Lymphoma) are eligible. Presentations of these histologies with substantial occurrence of malignant cells into the bloodstream (lymphocyte count ? x ^/L) including all leukemic presentations are excluded. Subjects with transformation of indolent lymphoma must have received therapy after a diagnosis of transformation that is appropriate for aggressive histology as described in . Other histologies are not eligible. Confirmation of relapsed or refractory aggressive B-cell non-Hodgkin lymphoma of the following histology at relapse: diffuse large B-cell lymphoma (DLBCL), not otherwise specified (NOS; de novo or transformed follicular lymphoma [tFL]), high-grade B-cell lymphoma with MYC and BCL and/or BCL rearrangements with DLBCL histology (double/triple hit lymphoma [DHL/THL]), and follicular lymphoma Grade B per WHO classification Histologically confirmed follicular lymphoma, grade -a. Previous history of indolent lymphoma treated with more than multi-agent chemotherapy regimen or previous cancer therapy for recurrent DLBCL or Grade b follicular lymphoma If the subjects has transformed DLBCL, the diagnosis is confirmed by biopsy and is immunohistologically characterized as transformation to DLBCL from indolent lymphoma (eg, follicular lymphoma). Histologically confirmed DLBCL expressing CD antigen; patients with transformed lymphoma are excluded; in this regard, patients with composite lymphoma in the diagnostic tissue (concomitant DLBCL and follicular or other low-grade lymphoma component) are excluded; however, patients with DLBCL in primary diagnostic tissue but a bone marrow that shows low grade or indeterminate lymphoma are eligible; patients with known primary mediastinal large B-cell lymphoma (PMLBCL) are excluded; similarly, patients with known c-myc translocation (by fluorescence in situ hybridization) positive DLBCL are encouraged to participate in trials specifically designed for these patients; however patients with known c-myc DLBC positive are NOT excluded from this study; c-myc testing prior to study enrollment is NOT required Treatment-naive patients with histologically confirmed systemic de novo or transformed diffuse large B-cell lymphoma (DLBCL) (from follicular or marginal zone lymphoma), or follicular lymphoma (FL) Grade b; Grade b follicular lymphoma Histologically confirmed previously untreated DLBCL or Grade B FL, [double-positive for BCL and c-MYC] or transformed lymphoma. Transformed lymphoma from FL or marginal zone lymphoma, but not chronic lymphocytic leukemia (CLL) [Richter Transformation] are allowed as long as no prior anti-lymphoma therapy of any kind has been administered. A diagnosis of follicular lymphoma (grades , , or a), untreated Grade b follicular lymphoma Patients with follicular lymphoma must have received at least two prior therapies Participants with transformed lymphoma Histologically confirmed marginal zone lymphoma or follicular lymphoma (grade , or a; CD+ by flow cytometry or histochemistry). Histology other than follicular or marginal zone lymphoma or clinical evidence of transformation or Grade b follicular lymphoma. Transformed DLBCL or DLBCL with coexistent histologies (eg, follicular or mucosa-associated lymphoid tissue lymphoma). Grade b follicular lymphoma Histologically confirmed CD+ follicular lymphoma, grade , , or a or marginal zone lymphoma Prior history of low grade lymphoma with transformation to DLBCL; if a patient has a composite diagnosis of DLBCL and low grade without a prior history of lymphoma, they will not be considered ineligible Histologically confirmed diagnosis of B-cell indolent Non-Hodgkin lymphoma with histological subtype limited to follicular lymphoma or marginal zone lymphoma, at initial diagnosis and without evidence of pathological transformation or clinical signs suggesting transformation Histologically confirmed diagnosis of follicular lymphoma grade b or transformed disease and chronic lymphocytic leukemia (CLL) Histologically confirmed follicular lymphoma grade , or a, Stage II-IV Symptomatic follicular lymphoma requiring treatment. Clinical evidence of transformed lymphoma or Grade b follicular lymphoma. For participants with follicular lymphoma: requirement for treatment according to Groupe d'Etude des Lymphomes Folliculaires (GELF) criteria Grade b follicular lymphoma, small lymphocytic lymphoma or Waldenstrm's macroglobulinaemia For participants with non-follicular lymphoma: prior treatment with chemotherapy or immunotherapy Diagnosis of DLBCL (de novo DLBCL, or transformed from indolent lymphoma) or follicular grade lymphoma on the basis of tissue biopsy. Patients with de novo DLBCL must have received - treatment regimens for DLBCL. Patients with follicular grade lymphoma must have received - treatment regimens for follicular lymphoma (any grade). Patients with DLBCL transformed from indolent lymphoma must have received at least - treatment regimens for NHL. Patient has histologically confirmed diagnosis of follicular lymphoma or Hodgkin lymphoma More than one prior line of any systemic chemoimmunotherapy for follicular lymphoma Transformed lymphoma Prior treatment for follicular lymphoma Indolent lymphoma including Grades -a follicular, small lymphocytic, lymphoplasmacytic, and marginal zone lymphoma; Stages III-IV, or bulky disease, Stage II. Tumor verified CD+ and CT imaging done at screening verifying disease Indolent lymphoma including grades -a follicular, small lymphocytic, lymphoplasmacytic, and marginal zone lymphoma; stages III-IV, or bulky disease stage II (i.e. as any single mass > cm in any direction) Grade b follicular lymphoma or evidence that the indolent lymphoma has transformed to aggressive lymphoma TIER I SUBJECTS: Histologically confirmed follicular lymphoma (grade , or ) by the World Health Organization (WHO) classification; all pathology must be confirmed at either Brigham and Women's Hospital or Massachusetts General Hospital; a repeat biopsy confirming the above histologies must be performed prior to enrollment if there is clinical suspicion that the patient has transformed to a more aggressive lymphoma TIER II SUBJECTS: Histologically confirmed follicular lymphoma (grade , or ) by the WHO classification; all pathology must be confirmed at either Brigham and Women's Hospital or Massachusetts General Hospital; a repeat biopsy confirming the above histologies must be performed prior to enrollment if there is clinical suspicion that the patient has transformed to a more aggressive lymphoma Any component of transformed follicular lymphoma Biopsy confirmed low-grade B-cell lymphoma, specifically, follicular grade or , or A marginal zone or small lymphocytic lymphoma; patients must have relapsed from or are refractory to prior therapy Transformation Follicular Lymphoma (TFL) for subjects with transformed FL must have received prior chemotherapy for follicular lymphoma and subsequently have chemorefractory disease after transformation to DLBCL Patients with confirmed CD-positive DLBCL or grade b follicular non-Hodgkin lymphoma (NHL). Biopsy confirmed, untreated, low-grade B-cell lymphoma, including follicular (Grade , , or A) [Harris, Swerdlow et al. ] or marginal, or CLL/SLL with lymph node involvement. Confirmed diagnosis of low tumor burden, CD-positive follicular lymphoma Diagnosis of CD+, follicular lymphoma that has not been treated CD-immunophenotyping of tumor to document B-cell follicular lymphoma Clinical evidence of transformation to a more aggressive subtype of lymphoma or grade B follicular lymphoma Pathologically confirmed diagnosis of mantle cell lymphoma, follicular lymphoma Grade , diffuse large B-cell lymphoma (DLBCL), including transformed follicular histology, Burkitt lymphoma, or B-lineage lymphoblastic lymphoma Follicular lymphoma Grades , , A follicular lymphoma (NCI CTCAE grade or ) Inclusion Criteria:\n\n . Previously untreated stage IV indolent B-cell lymphoma [Amendment May :\n eligibility restricted to follicular lymphoma]\n\n . Age <\n\n Exclusion Criteria: Histologically confirmed relapsed or refractory CD+ DLBCL, transformed indolent lymphoma (follicular or other), or primary mediastinal large B-cell lymphoma; Patients with follicular, grade or non-Hodgkin lymphoma with a FLIPI (Follicular Lymphoma International Prognostic Index) score of -, with no anticipated need for treatment within the next months are considered eligible for this study, regardless of previous treatment history Patients with transformed lymphoma (e.g., Richter's transformation arising in follicular lymphoma or chronic lymphocytic leukemia) Chemo-refractory DLBCL (including transformed low grade lymphoma) Follicular lymphoma Grade B Patients with transformed lymphoma (e.g., Richter's transformation arising in follicular lymphoma or chronic lymphocytic leukemia) Patients with transformed lymphoma (e.g., Richters transformation arising in follicular lymphoma or chronic lymphocytic leukemia) Follicular variant