An Early Phase Study of Venetoclax, Lenalidomide, and Rituximab/Hyaluronidase in Slow-Growing Lymphomas That Have Come Back After Treatment or Have Not Responded to Treatment

Inclusion Criteria: Signed informed consent form * Ability and willingness to comply with the requirements of the study protocol * Able to swallow oral medications whole * Patients must have received at least one prior systemic therapy * Histologically confirmed indolent B-cell non-Hodgkin's lymphoma (NHL) of any of the following subtypes recognized by the World Health Organization (WHO) classification: Follicular lymphoma and marginal zone lymphoma. Patients with indolent non-Hodgkin's Lymphoma (iNHL) should have received at least 1 previous prior therapy * Patients must have an indication for treatment by Groupe d'Etude des Lymphomes Folliculaires (GELF) criteria 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 * All study participants must be registered into the mandatory lenalidomide 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 lenalidomide 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. Inability to take any form of prophylaxis excludes participation * Eastern Cooperative Oncology Group performance status of 0, 1, or 2 * Hemoglobin \>= 9 g/dL (unless caused by underlying disease, as established by extensive bone marrow involvement or as a result of hypersplenism secondary to the involvement of the spleen by lymphoma per the investigator) * Absolute neutrophil count \>= 1.0 x 10\^9/L (unless caused by underlying disease, as established by extensive bone marrow involvement or as a result of hypersplenism secondary to the involvement of the spleen by lymphoma per the investigator) * Platelet count \>= 75 x 10\^9/L (unless caused by underlying disease, as established by extensive bone marrow involvement or as a result of hypersplenism secondary to the involvement of the spleen by lymphoma per the investigator) * International normalized ratio \> 1.5 x upper limit of normal (ULN) for patients not receiving therapeutic anticoagulation * Partial thromboplastin time (PTT) or activated PTT (aPTT) =\< 1.5 x ULN * Creatinine clearance \>= 60 mL/min, calculated with the use of the 24-hour creatinine clearance or modified Cockcroft-Gault equation * Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) =\< 2.5 x ULN * Total bilirubin =\< 1.5 x ULN (or =\< 3 x ULN for patients with documented Gilbert syndrome) * Women of childbearing potential must have a negative serum or urine pregnancy test result within 14 days prior to registration * For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use a contraceptive method with a failure rate of \< 1% per year during the treatment period and for at least 30 days after the last dose of venetoclax and lenalidomide or 12 months after the last dose of rituximab, whichever is longer \* Women must refrain from donating eggs during this same period \* A woman is considered to be of childbearing potential if she is postmenarcheal, has not reached a postmenopausal state (\>= 12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (removal of ovaries and/or uterus) \* Examples of contraceptive methods with a failure rate of \< 1% per year include bilateral tubal ligation, male sterilization, hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices \* The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not acceptable methods of contraception * For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures, and agreement to refrain from donating sperm, as defined below: \* With female partners of childbearing potential, men must remain abstinent or use a condom plus an additional contraceptive method that together result in a failure rate of \< 1% per year during the treatment period and for at least 6 months after the last dose of rituximab and for at least 30 days after the last dose of venetoclax and lenalidomide whichever is longer. Men must refrain from donating sperm during this same period \* With pregnant female partners, men must remain abstinent or use a condom during the treatment period and for at least 6 months after the last dose of rituximab to avoid exposing the embryo \* The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not acceptable methods of contraception Exclusion Criteria: Known hypersensitivity to any of the study drugs study drugs * Known central nervous system (CNS) involvement by lymphoma * Prior allogeneic stem cell transplant is not permitted if patient is fewer than 4 months from transplant and has either active graft versus host disease or on immunosuppression * History of severe allergic reactions to humanized monoclonal antibodies * Prior use of lenalidomide or venetoclax or other BCL2 family inhibitors; prior rituximab is allowed as long as they continue to express CD20 and are not rituximab refractory as defined as: \* Did not respond (at least a partial response \[PR\]) to rituximab or rituximab (R)-chemoregimen therapy \* Time to disease progression \< 6 months after last rituximab dose * 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 * Evidence of significant, uncontrolled concomitant diseases that could affect compliance with the protocol or interpretation of results or that could increase risk to the patient, including renal disease that would preclude chemotherapy administration or pulmonary disease (including obstructive pulmonary disease and history of bronchospasm) * 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 to registration * 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 registration: \* Steroid therapy for anti-neoplastic intent \* 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 Presence of positive test results for hepatitis B virus (HBV), hepatitis B surface antigen (HBsAg), or hepatitis C (HCV) antibody \* Patients who are positive for HCV antibody must be negative for HCV by polymerase chain reaction (PCR) to be eligible for study participation \* Patients with occult or prior HBV infection (defined as positive total hepatitis B core antibody \[HBcAb\] and negative HBsAg) may be included if HBV deoxyribonucleic acid (DNA) is undetectable. These patients must be willing to undergo monthly DNA testing. * Known infection with human immunodeficiency virus (HIV) or human T-cell leukemia virus 1 (HTLV-1) * 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 * Pregnant or lactating, or intending to become pregnant during the study * Recent major surgery (within 6 weeks prior to the start of cycle 1, day 1) other than for diagnosis * Malabsorption syndrome or other condition that precludes enteral route of administration * Known allergy to both xanthine oxidase inhibitors and rasburicase