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