Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible; however, HIV patients treated with regimens that have low cytochrome P (CYP) inhibition may be allowed as long as the patients general health and cluster of differentiation (CD) counts are within acceptable levels Patients who are known to be human immunodeficiency virus (HIV)-positive at registration are eligible at the time of registration:\r\n. Cluster of differentiation (CD)+ cell count greater or equal to cells/mm^\r\n. If patient is on antiretroviral therapy, there must be minimal interactions or overlapping toxicity of the antiretroviral therapy with the experimental cancer treatment; once daily combinations that use pharmacologic boosters may not be used\r\n. No history of non-malignancy acquired immunodeficiency syndrome (AIDS)-defining conditions other than historical low CD+ cell counts Patients with a known history of human immunodeficiency virus (HIV) seropositivity:\r\n* Must have undetectable viral load using standard HIV assays in clinical practice\r\n* Must have cluster of differentiation (CD) count >= /mcL\r\n* Must not require prophylaxis for any opportunistic infections (i.e., fungal, Mycobacterium avium complex [mAC], or pneumocystis jiroveci pneumonia [PCP] prophylaxis)\r\n* Must not be newly diagnosed within months prior to sub-study registration Known human immunodeficiency virus (HIV)-positive patients should have a cluster of differentiation (CD) count > /mm^ Human immunodeficiency (HIV) positive (+) patients are eligible provided they meet the other eligibility criteria and:\r\n* Cluster of differentiation (CD)+ cells are >= /mm^\r\n* There is no history of acquired immunodeficiency syndrome (AIDS) defining conditions other than historically low CD+ cell count\r\n* The following antiretroviral agents are not allowed: zidovudine, stavudine, protease inhibitors, non-nucleoside reverse transcriptase inhibitors, combination pills with pharmacologic boosters\r\n* Recommended antiretroviral regimens to avoid pharmacokinetic (PK) interactions include strand integrase inhibitors with nucleoside reverse transcriptase inhibitors (for example, dolutegravir given with tenofovir and emtricitabine) Disease must be cluster of differentiation (CD) positive Patients with known human immunodeficiency virus (HIV) positive must have a cluster of differentiation (CD) cell count be >= cells/mm^ within days prior to study entry (note, however, that HIV testing is not required for entry into this protocol) A cluster of differentiation (CD)+ lymphocyte count > /mcL will be required within weeks of study participation On continuous antiretrovirals with cluster of differentiation (CD) count > cells/ml with sustained undetectable viral load for at least months; (HIV positive women) Prior treatment with Cluster of differentiation (CD) antibody Further exclusion criteria apply. AIDS defined as a CD (cluster of differentiation ) count less then in the context of HIV sero-positivity or chronically is taking immunosuppressive medication such as steroids or transplant related medications. For non-myeloablative transplants, >= % cluster of differentiation (CD) donor chimerism at screening Cluster of differentiation (CD) count >= within days prior to enrollment or plasma HIV- RNA < copies/mL within days prior to randomization Use of rituximab and other anti-cluster of differentiation antigen (CD) antibodies known to have the same epitope as rituximab or anti-cluster of differentiation antigen (CD) for which the epitope is unknown within months prior to enrollment; Patients must have at least x ^ cluster of differentiation (CD)+ cells/kg frozen Have previously received or are ineligible for treatment with blinatumomab; ineligibility will include (but not be limited to) cluster of differentiation (CD)-negative disease, denial of insurance coverage, physician discretion, and/or patient refusal Histologically confirmed diagnosis of cluster of differentiation (CD)-positive ALCL with documented ALK-positive status Cluster of differentiation (CD) count >= /uL or >= % of peripheral blood lymphocytes Patients with well controlled human immunodeficiency virus (HIV) infection are eligible if their cluster of differentiation (CD) count is > /cu mm and viral load is < copies/ml Patients with known human immunodeficiency virus (HIV) infection are eligible if not on antiviral agents and cluster of differentiation (CD) counts are adequate (>= ) Availability of >= . million cluster of differentiation (CD)+ cells/kg previously apheresed Patient has a confirmed diagnosis of mantle cell lymphoma with B-lymphocyte antigen cluster of differentiation (CD) (CD) positivity in tissue biopsy Human immunodeficiency virus (HIV) positive (+) patients with cluster of differentiation (CD) counts >= cells/mm^ on anti-viral therapy Patients who have known human immunodeficiency virus (HIV) positivity must be on a -drug antiviral regimen that does not include zidovudine, and must have a cluster of differentiation (CD) count > /mm^ and virus load < copies/ml, and are placed on a regimen to prevent pneumocystis pneumonia (PCP) reactivation during treatment INCLUSION CRITERIA FOR ENROLLMENT: Donor cluster of differentiation (CD)+ chimerism >= % measured in peripheral blood or bone marrow Patients must have primary refractory or first relapse of cluster of differentiation (CD)+ Hodgkin lymphoma Known sensitivity to lenalidomide or other thalidomide derivatives or anti cluster of differentiation (CD) Cluster of differentiation (CD) count >= /uL or >= % of peripheral blood lymphocytes Relapsed/refractory MCL: Confirmed diagnosis of mantle cell lymphoma with cluster of differentiation (CD) and cyclin D through cyclin D positivity in tissue biopsy Must have - x ^ cluster of differentiation (CD)+ cells/kg (recipient weight) infused on day A minimum of x ^ cluster of differentiation positive (CD+) cells must have been collected Patients with acquired immunodeficiency syndrome (AIDS-related illnesses) or known human immunodeficiency virus (HIV) disease must:\r\n* Have a cluster of differentiation (CD) count >= cells/uL within days before beginning study therapy\r\n* Be off all antiretroviral therapy (prophylaxis/treatment) more than days before beginning study therapy, and\r\n* Have no evidence of opportunistic infections Patients must have cluster of differentiation (CD) positivity of >= % Cluster of differentiation (CD) count >= /uL Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are eligible; unless the patients cluster of differentiation (CD)+ count is below the institutional lower limit of normal Patients with a known history of human immunodeficiency virus (HIV) seropositivity: must have undetectable viral load using standard HIV assays in clinical practice; must have cluster of differentiation (CD) count >= /mcL; must not require prophylaxis for any opportunistic infections (i.e., fungal, mycobacterium avium complex [mAC], or pneumocystis pneumonia [PCP] prophylaxis); must not be newly diagnosed within months prior to re-registration Patients with a known history of human immunodeficiency virus (HIV) seropositivity: . Must have undetectable viral load using standard HIV assays in clinical practice; . Must have cluster of differentiation (CD) count >= /mcL; . Must not require prophylaxis for any opportunistic infections (i.e., fungal, mycobacterium avium complex [mAC], or pneumocystis pneumonia [PCP] prophylaxis); . Must not be newly diagnosed within months prior to re-registration Patients with a known history of human immunodeficiency virus (HIV) seropositivity:\r\n* Must have undetectable viral load using standard HIV assays in clinical practice\r\n* Must have cluster of differentiation (CD) count >= /mcL\r\n* Must not require prophylaxis for any opportunistic infections (i.e., fungal, mycobacterium avium complex [mAC], or pneumocystis pneumonia [PCP] prophylaxis)\r\n* Must not be newly diagnosed within months prior to re-registration Patients with any stage of pathologically confirmed cluster of differentiation (CD)+ acute, lymphoma, chronic, or smoldering subtypes of ATLL Subjects must be on a prophylactic regimen for Pneumocystis carinii pneumonia, or agree to begin such treatment and remain on treatment until after completion of therapy and until the cluster of differentiation (CD) cells are greater than /mm^ Patients with known human immunodeficiency virus (HIV) are not eligible if cluster of differentiation (CD) count is =< cell/mm^ or if receiving antiretroviral therapy Patients with known human immunodeficiency virus (HIV) who have cluster of differentiation (CD)+ T cell counts >= cells/mm^ and who do not require antiretroviral therapy are eligible Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible; if an HIV-positive patient has adequate cluster of differentiation (CD) counts (CD above the lower limit of institutional normal) and is on antiretroviral therapy with newer agents, which are not strong cytochrome (CYP) inhibitors, they will be eligible Human immunodeficiency virus (HIV)-positive patients on antiviral drugs and/or cluster of differentiation (CD) count is inadequate (< ); if neither condition exists, HIV-positive patients are eligible Patients with a history of prior treatment with ipilimumab, anti-programmed cell death (PD ) antibody, cluster of differentiation (CD) agonist or other immune activating therapy such as anti-cluster of differentiation (CD ) antibody Cluster of differentiation (CD) count > cells/mm^ Immunocompromised patients (other than that related to the use of corticosteroids) including patients known to be human immunodeficiency virus (HIV) positive with cluster of differentiation (CD) counts < Lymphopenia, cluster of differentiation (CD) lymphopenia, leukopenia, and anemia will not render patients ineligible Histologically documented cluster of differentiation (CD) positive lymphoma Patients who are known to be human immunodeficiency virus (HIV) positive must have a normal cluster of differentiation (CD) count and undetectable viral load Participants must have previously untreated cluster of differentiation (CD) -positive diffuse large, B-cell lymphoma B-cell hematologic malignancies expected to express the cluster of differentiation (CD) antigen who have relapsed after or failed to respond to at least one prior treatment regimen and for whom there is no available therapy expected to improve survival Cluster of differentiation (CD) count >= /mcL Human immunodeficiency virus (HIV)-positive patients with inadequate cluster of differentiation (CD) counts or those who are on combination antiretroviral therapy with strong cytochrome P, family , subfamily A, polypeptide (CYPA) effects are ineligible for this trial Subjects must have measurable disease defined as at least one tumor lesion of at least . cm or a peripheral blood cluster of differentiation (CD)+, CD+ lymphocyte count of at least , cells/uL Patients with a diagnosis of active human immunodeficiency virus (HIV) infection, on anti-retroviral therapy, or with a cluster of differentiation (CD) count less than are ineligible; testing is not required in the absence of clinical findings or suspicion Patients with human immunodeficiency virus (HIV) are eligible if they are not on antiviral agents and have adequate cluster of differentiation (CD) counts (>= mm^) Human immunodeficiency virus (HIV)-positive patients with cluster of differentiation (CD) counts less than the lower limit of institutional normal Known diagnosis of human immunodeficiency virus (HIV) infection unless patient is fully immunocompetent (cluster of differentiation [CD] > ) and patient is not taking antiretroviral therapy Immunocompromised patients (other than that related to the use of corticosteroids) with the exception of patients known to be human immunodeficiency virus (HIV) positive and have a cluster of differentiation (CD) count > and do not require antiretroviral therapy Expansion Cohort: patients who have known human immunodeficiency virus (HIV) positivity must be on a -drug antiviral regimen that does not include zidovudine and must have a cluster of differentiation (CD) count > /mm^ and virus load < copies/mL; they must be placed on a regimen to prevent pneumocystis pneumonia (PCP) reactivation during treatment Patients with HCL variant (as defined by absence of expression of cluster of differentiation [CD] or absence of BRAF VE mutation) Documented cluster of differentiation (CD)+ expression from either original diagnosis or a tumor biopsy in the relapsed setting Patients with human immunodeficiency virus (HIV) infection are eligible provided their cluster of differentiation (CD) count is greater than or equal to the institutional lower limit of normal (LLN) (>= cells/uL) Tumor cell negative for cluster of differentiation (CD) (absence of result due to technical problems in the presence of other characteristics suggestive of BL/DLBCL, including genetic and phenotypic features, is not an exclusion criteria) Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy will be eligible unless the cluster of differentiation (CD) count is < cells/mm^ within one month of study enrollment Previous treatment with SGN- or any other prior anti-cluster of differentiation (CD)-based antibody therapy Patients with human immunodeficiency virus (HIV) disease will be permitted, only if they are on effective anti-retroviral therapy, have a cluster of differentiation (CD) count greater than , and have had no opportunistic infections within the past months Patients must provide a lymph node sample of at least . cm in the long axis, or a bone marrow aspiration sample providing at least million cluster of differentiation (CD) and/or CD+ (approximately ml) History of histologically documented, B-lymphocyte antigen cluster of differentiation plus (CD+), iNHL Patients with cluster of differentiation (CD) selected auto grafts Positive for cluster of differentiation (CD) via immunophenotyping Histologically confirmed DLBCL, cluster of differentiation (CD) positive by flow or immunohistochemistry (IHC); transformed DLBCL is allowed as long as no prior therapy has been given Lymphoblasts may have any positive expression of cluster of differentiation (CD) for ofatumumab administration Human immunodeficiency virus (HIV)-infected persons are eligible if they meet other eligibility criteria including the following:\r\n* No prior acquired immune deficiency syndrome (AIDS)-defining condition other than cluster of differentiation (CD)+ cells nadir < /mm^\r\n* Pre-leukemia CD+ cell count >= /mm^\r\n* Willing to adhere to antiretroviral therapy regimen with minimal overlapping toxicity and PK interactions with the experimental agents in this study; no zidovudine- and no ritonavir-containing regimens and no -drugs-in- pill regimens containing pharmacologic boosters are allowed; recommended regimens are integrase inhibitors combined with tenofovir and emtricitabine Patients with cluster of differentiation (CD) positive diffuse large B-cell lymphoma as confirmed by a pathological biopsy report A cluster of differentiation (CD)+ lymphocyte count > /mcL will be required within weeks of study participation Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are eligible, unless the patients cluster of differentiation (CD) count is below the institutional lower limit of normal, or the patient is taking prohibited CYPA/ strong inhibitors or inducers Lymphopenia, cluster of differentiation (CD) lymphopenia, leukopenia, and anemia will not render patients ineligible Patients must have relapsed or refractory cluster of differentiation (CD) + lymphoid malignancies with either documented central nervous system (CNS) involvement or peripheral nerve infiltration If HIV-positive, any cluster of differentiation (CD) count will be allowed on study Human immunodeficiency virus (HIV)-positive patients on antiretroviral medications that are CYPA substrates will be closely monitored; HIV-positive patients will be excluded if they have a cluster of differentiation (CD) count < Autologous transplant eligible patients must have histologically or cytologically confirmed cluster of differentiation (CD) positive relapsed or refractory DLBCL by biopsy within days prior to subject enrollment and must have been previously treated with an anthracycline and rituximab-containing regimen Immunocompromised patients (other than that related to the use of corticosteroids) including patients known to be human immunodeficiency virus (HIV) positive with low cluster of differentiation (CD) count; Note: previous calcineurin inhibitor or previous sirolimus use allowed If human immunodeficiency virus (HIV) positive, cluster of differentiation (CD) count must be >= A cluster of differentiation (CD) count > /mcL will be required within weeks of study participation Documented Cluster of Differentiation Antigen (CD) + B-Cell Chronic Lymphocytic Lymphoma (B-CLL) Histopathologic confirmation of one of the following cluster of differentiation antigen positive (CD+) B-cell non-Hodgkin's lymphomas (tissue diagnostic procedures must be performed within months of study entry and with biopsy material available for review): Newly diagnosed cluster of differentiation (CD) + DLBCL with IPI between - Human immunodeficiency virus (HIV)-positive patients who are not receiving: agents with the potential for PK interactions with romidepsin or hepatotoxic antiretrovirals (nucleoside reverse-transcriptase inhibitors [NRTIs]: abacavir, didanosine, emtricitabine, lamivudine, stavudine, and zidovudine), dual protease inhibitor (PI)-based regimens except low-dose boosting with ritonavir, atazanavir, indinavir, maraviroc, and nevirapine may be eligible; additionally, the HIV-positive patients should have a cluster of differentiation (CD) count > /mm^; if the specific cause of hepatic dysfunction is unknown, the patient should be worked up for other viral causes of hepatitis and their eligibility determined after consultation with the principal investigator