Brentuximab Vedotin, Bendamustine, and Rituximab in Patients With Relapsed or Refractory B-cell Non-Hodgkin Lymphoma

Inclusion Criteria: * CD30 detectable B lineage relapsed refractory NHL including the following histologies: * Aggressive lymphomas: diffuse large B cell lymphoma, primary mediastinal B cell lymphoma, grey zone lymphomas, high grade B cell lymphomas, and transformed indolent lymphomas * 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: * The Groupe d'Etude des Lymphomes Folliculaires (GELF) criteria * Intermediate or high risk by Follicular Lymphoma International Prognostic Index (FLIPI) score or elevated lactose dehydrogenase (LDH)/ beta-2 microglobulin (B2M) * Subjects between 18 and 75 years old. Subjects older than 75 years old to be discussed with PI prior to subject consent; consensus between PI and treating physician is required. * Karnofsky performance status (KPS) \>= 70%, Eastern Cooperative Oncology Group (ECOG) =\< 2 * At least 1 measurable site of disease according to Revised Response Criteria for Malignant Lymphoma * Patients must have received at least one but no more than 4 prior lines of systemic therapy * American Heart Association (AHA) class 1 without significant limitation of physical activity * Ejection fraction (EF) of at least \>= 40% by multigated acquisition (MUGA) or echocardiography (ECHO) * Total bilirubin =\< 1.5 mg/dl * Alanine aminotransferase (ALT), aspartate aminotransferase (AST) less than 2.5 times the upper limit of normal without evidence of active infectious hepatitis * Creatinine clearance \>= 40 ml/min * Platelets \> 75,000 cells/ul * Absolute neutrophil count (ANC) \> 1,000 cells/ul * Ability to provide informed consent * Females of childbearing potential must have a negative serum or urine beta-human chorionic gonadotropin (HCG) pregnancy test at screening; pregnancy testing is not required for: (a) women who have been post-menopausal for at least 2 years without menses; or (b) women who are surgically sterile (e.g. by means of hysterectomy, tubal ligation, etc.) * Males and females of childbearing potential must be able and willing to use an effective contraceptive method during treatment and for three months after completing treatment Exclusion Criteria: * Active infections (bacterial, fungal, or viral) * Evidence of sanctuary site involvement by disease, e.g., central nervous system, ocular, testicular involvement * Evidence of second malignancy, abnormal cytogenetics, or morphologic evidence of myelodysplastic syndromes (MDS) * Recent chemotherapy within 3 weeks of screening * Major surgery within 4 weeks of screening * Diagnosed or treated for malignancy other than NHL for which patient will be treated, except: malignancy treated with curative intent and with no known active disease present for \>= 3 years before subject registration; adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease; adequately treated carcinoma in situ without evidence of disease * History of stroke or intracranial hemorrhage within 6 months prior to registration * Requires anticoagulation with warfarin or equivalent vitamin K antagonists * Requires treatment with strong cytochrome (CYP3A4/5) inhibitors * Clinically significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 6 months of screening, or any class 3 (moderate) or class 4 (severe) cardiac disease as defined by the New York Heart Association Functional Classification * Known history of human immunodeficiency virus or active hepatitis C virus or active hepatitis B virus infection or any uncontrolled active systemic infection requiring intravenous antibiotics * Women who are pregnant or breastfeeding * Prior use of brentuximab vedotin * Prior use of bendamustine for indolent lymphoma allowed if \> 2 years, CR to bendamustine and well tolerated with no residual \> grade 1 toxicity; no prior use of bendamustine for aggressive lymphoma allowed * Prior allogeneic transplant * Patients with Child-Pugh B or C hepatic impairment