Obinutuzumab, Venetoclax, and Lenalidomide in Treating Patients With Relapsed or Refractory B-cell Non-Hodgkin Lymphoma

Inclusion Criteria: * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Prior venetoclax or other BCL-2 family inhibitors or prior lenalidomide is not permitted * Creatinine clearance \>= 50 ml/min using a 24 hour creatinine clearance or estimated creatinine clearance using the Cockcroft-Gault equation * Bilirubin =\< 1.5 x upper limit of normal (ULN) unless due to Gilbert's syndrome * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 3 x ULN * Absolute neutrophil count (ANC) \>= 1000/mm\^3 * Platelet \>= 75,000/mm\^3 * Unless related to bone marrow involvement with disease, in which case platelets must be \>= 50,000/mm\^3 * Recovery to =\< grade 1 from all toxicities associated with prior therapy except alopecia * Histologically confirmed B-cell non-Hodgkin's lymphoma (NHL) of any of the following subtypes recognized by the World Health Organization (WHO) classification: Burkitt lymphoma, B-cell lymphoma unclassifiable with features intermediate between diffuse large B-cell lymphoma and Burkitt lymphoma, diffuse large B-cell lymphoma, marginal zone lymphoma, or follicular lymphoma; patients with evidence of histological transformation to diffuse large B-cell lymphoma from indolent NHL are eligible * At least one prior therapy; prior autologous stem cell transplant is permitted; patients with aggressive lymphoma who have not received high-dose therapy (HDT)/autologous stem cell transplantation (ASCT) must be ineligible for HDT/ASCT; prior allogeneic stem cell transplant is not permitted * Patients with indolent lymphoma must have an indication for treatment in the opinion of the investigator * Radiographically measurable disease by computed tomography (CT) scan, defined as at least one node \> 1.5 cm in size or assessable disease * All study participants must be registered into the mandatory Revlimid risk evaluation and mitigation strategy (REMS) program, and be willing and able to comply with the requirements of the REMS program * Females of reproductive potential must adhere to the scheduled pregnancy testing as required in the Revlimid REMS program * Able to take aspirin (81 or 325 mg) daily as prophylactic anticoagulation (patients intolerant to aspirin (ASA) may use low molecular weight heparin or equivalent) * EXPANSION COHORT * Cohort A will enroll 10 patients with a diagnosis of diffuse large B-cell lymphoma; B-cell lymphoma unclassifiable with features intermediate between diffuse large B-cell lymphoma and Burkitt lymphoma (double hit lymphoma), Burkitt lymphoma, and transformed lymphoma * Cohort B will enroll 20 patients with a diagnosis of follicular lymphoma, grade 1-2 and 3A; grade 3B is excluded; diagnoses made by a fine needle aspirate or bone marrow biopsy alone are not permitted Exclusion Criteria: * Patients with active central nervous system (CNS) involvement with lymphoma are not eligible * Patients with human immunodeficiency virus (HIV) or human T-cell leukemia virus 1 (HTLV-1) are not eligible * Evidence of active hepatitis B infection, based on positive surface antigen or hepatitis B deoxyribonucleic acid (DNA) polymerase chain reaction (PCR), or active hepatitis C infection; patients who are hepatitis B core antibody positive must take prophylaxis with lamivudine or equivalent and be willing to undergo monthly hepatitis B DNA PCR testing * Prior allogeneic stem cell transplant is not permitted * Unable to swallow capsules or malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel or ulcerative colitis, symptomatic inflammatory bowel disease, or partial or complete bowel obstruction likely to interfere with the delivery, absorption, or metabolism of venetoclax or lenalidomide * Any chemotherapy or radiation therapy within 4 weeks of the first dose of study drug * Patients may take steroids for disease control up to 24 hours prior to study enrollment * Any illness, medical condition or organ system dysfunction which, in the investigator's opinion, could compromise the subject's safety, interfere with the absorption or metabolism of venetoclax and lenalidomide, or put the study outcomes at undue risk * A cardiovascular disability status of New York Heart Association class \>= 2 * History of severe allergic reactions to humanized monoclonal antibodies * History of other malignancy that could affect compliance with the protocol or interpretation of results; patients with a history of curatively treated basal or squamous cell carcinoma or stage 1 melanoma of the skin or in situ carcinoma of the cervix are eligible; patients with a malignancy that has been treated with surgery alone with curative intent will also be excluded; individuals in documented remission without treatment for \>= 2 years prior to enrollment may be included at the discretion of the investigator * Known hypersensitivity to any of the study drugs or analogs * Known active bacterial, viral, fungal, mycobacterial, parasitic, or other infection (excluding fungal infections of nail beds) at study enrollment, or any major episode of infection requiring treatment with IV antibiotics or hospitalization (relating to the completion of the course of antibiotics) within 4 weeks prior study therapy * Requires the use of warfarin (because of potential drug-drug interactions that may potentially increase the exposure of warfarin) * Received the following agents within 7 days prior to the first dose of venetoclax: * Strong and moderate CYP3A inhibitors * Strong and moderate CYP3A inducers * Consumed grapefruit, grapefruit products, Seville oranges (including marmalade containing Seville oranges), or star fruit within 3 days prior to the first dose of venetoclax * Clinically significant history of liver disease, including viral or other hepatitis, current alcohol abuse, or cirrhosis * Receipt of live-virus vaccines within 28 days prior to the initiation of study treatment or need for live-virus vaccines at any time during study treatment * Recent major surgery (within 6 weeks prior to the start of study treatment) other than for diagnosis * Malabsorption syndrome or other condition that precludes enteral route of administration * Known allergy to both xanthine oxidase inhibitors and rasburicase * Pregnant or lactating, or intending to become pregnant during the study