Venetoclax With Obinutuzumab and Magrolimab (VENOM) in Relapsed and Refractory Indolent B-cell Malignancies

* INCLUSION CRITERIA: * Patients must have a confirmed histologic diagnosis of an indolent cluster of differentiation 20 (CD20) positive B-cell lymphoma according to the criteria established by the 2016 version of the World Health Organization (WHO) classification system. Lymphomas with any prior CD20 expression (by immunohistochemistry or flow cytometry) will be considered eligible. Diagnosis must be confirmed by Laboratory of Pathology, National Cancer Institute (NCI) and the following indolent B-cell lymphomas are included: * Follicular lymphoma (FL): must be grade 1-2 or 3a * Marginal zone lymphoma (MZL) * Mantle cell lymphoma (MCL) * Chronic lymphocytic leukemia (CLL) * Participant must have relapsed and/or refractory disease, as defined below: * FL: relapsed after and/or refractory to at least two (2) prior lines of therapy with at least one of those therapies containing an anti-CD20 monoclonal antibody. NOTE: Participants with FL may be eligible after one (1) prior line of therapy if they have either: * Follicular lymphoma international prognostic index (FLIPI) \>=2 (120) * Disease progression within 24 months of the end of last therapy (POD24) * MZL: relapsed after and/or refractory to at least two (2) prior lines of therapy, with at least one containing an anti-CD20 monoclonal antibody. * MCL: relapsed after and/or refractory to at least two (2) prior lines of therapy, with at least one containing an anti-CD20 monoclonal antibody. NOTE: Participants with MCL may be eligible after one (1) prior line of therapy if they have either: * Blastoid or pleomorphic histology * 17p deletion * Tumor protein p53 (TP53) mutation or deletion * Antigen Kiel 67 (Ki67) \>=30% * Received a Bruton tyrosine kinase (BTK) inhibitor as first line therapy * CLL: relapsed after and/or refractory to at least two (2) prior lines of therapy. Participants with CLL are not required to have had therapy containing anti-CD20. NOTE: Participants with CLL may be eligible after one (1) prior line of therapy if they have either: * 17p deletion * TP53 mutation or deletion * Received both a Bruton's Tyrosine Kinase (BTK) inhibitor AND a B-cell lymphoma 2 (BCL2) inhibitor as first line therapy NOTE: Participants must not have received prior treatment with a cluster of differentiation 47 (CD47) or signal regulatory protein (SIRP) targeting agent -Adequate tissue from diagnostic biopsy (archival or fresh) must be available for performance of correlative studies NOTE: Tumor tissue may be from any previously collected tissue and adequacy is at the discretion of the Principal Investigator. If prior tissue is not available, patient must be willing to undergo baseline tissue biopsy (for patients with known or suspected bone marrow involvement, bone marrow may be acceptable tissue per discretion of the investigator). -Patients must have at least evaluable disease as assessed by clinical exam (i.e., palpable lymphadenopathy, measurable skin lesions, etc.), laboratory assessment (i.e., lymphoma involvement of bone marrow or peripheral blood by morphology, cytology or flow cytometry), and/or imaging (measurable lymph nodes or masses on computed tomography (CT) or magnetic resonance imaging (MRI) and/or evaluable fludeoxyglucose-18 (FDG)-avid lesions on positron emission tomography (PET). Patients may also have measurable disease. NOTE: Patients with known active central nervous system (CNS) lymphoma are not eligible. \- Age greater than or equal to 18 years NOTE: Because no dosing or adverse event data are currently available on the use of magrolimab in patients \<18 years of age, children are excluded from this study * Eastern Cooperative Oncology Group (ECOG) performance status less than or equal to 2 * Adequate organ function as evidenced by the following laboratory parameters: * Absolute neutrophil count (ANC): greater than or equal to 1,000/mm(3) * Platelets: greater than or equal to 50,000/mcL (transfusions permitted) * Hemoglobin: greater than or equal to 9 g/dL (transfusions permitted). NOTE: Patients must have required fewer than 2 units of red blood cell (RBC) transfusion in the 4 weeks prior to screening. Additional transfusions after screening and prior to enrollment are acceptable. * Renal function: Glomerular filtration rate (GFR) greater than or equal to 30 mL/min/1.73 m(2) as estimated by the Modification of Diet in Renal Disease (MDRD) abbreviated formula. If not on target, a 24-hour urine creatinine clearance can be used to directly measure. * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT): less than or equal to 3.0 x the upper limit of normal (ULN) NOTE: Patients with liver involvement with lymphoma less than or equal to 5.0 x ULN -Bilirubin less than or equal to 1.5 X ULN NOTE: Patients with Gilbert's syndrome may have a bilirubin level \> 1.5 X ULN, per discretion of the investigator -The effects of the study drugs on the developing human fetus are unknown. For this reason, women of childbearing potential (WOCBP) and men must agree to use effective contraception when sexually active. This applies for the time period between signing of the informed consent form and for the following time frames after the last dose of drug, whichever is later: 90 days after the last dose of magrolimab, 30 days after the last dose of venetoclax, and 18 months after the last dose of obinutuzumab for women and 6 months after the last dose of obinutuzumab for men. Men should refrain also from donating sperm for these same timeframes, and women must also refrain from donating eggs. NOTE: WOCBP is defined as any female who has experienced menarche and who has not undergone successful surgical sterilization or who is not postmenopausal (i.e., amenorrheic for \>12 months without alternative medical cause; post-menopausal status in females under 55 years of age should be confirmed with a serum follicle-stimulating hormone \[FSH\] level within applicable local laboratory reference range for postmenopausal women). Permanent sterilization methods include but are not limited to hysterectomy, bilateral salpingectomy and bilateral oophorectomy. The investigator or a designated associate is requested to advise the patient how to achieve highly effective birth control (failure rate of less than 1%), e.g., intrauterine device (IUD), intrauterine hormone-releasing system (IUS), bilateral tubal occlusion, vasectomized partner and sexual abstinence. The use of condoms by male patients is required unless the female partner is permanently sterile. * Ability of patient to understand and the willingness to sign a written informed consent document * Patients with prior autologous or allogeneic stem cell transplantation are potentially eligible if transplanted \> 6 months ago, and no active graft-vs-host disease requiring immunosuppressants. EXCLUSION CRITERIA: * Concomitant use of any investigational anti-lymphoma treatment * Known primary or acquired immunodeficiency syndrome (e.g., HIV) or known infection with human T-cell leukemia virus 1 (HTLV1). NOTE: HIV-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with the study drugs. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. In the future, appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated. * History of hemolytic anemia or autoimmune thrombocytopenia in the 3 months prior to enrollment. Patients with positive Direct Agglutination Test (DAT) but no evidence of clinically active hemolysis are eligible. * Hepatitis B surface antigen or hepatitis B deoxyribonucleic acid (DNA) polymerase chain reaction (PCR) positive. NOTE: Subjects who are hepatitis B core antibody positive will need to have a negative hepatitis B virus (HBV) DNA PCR result before enrollment. Those with a positive PCR for hepatitis B are excluded. * Pregnant or breastfeeding patients. NOTE: Pregnant women are excluded in this study because of the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with the study drugs, breastfeeding should be discontinued. * Requirement to continue on any of the medications that have significant potential for drug-drug interactions with the study regimen. For example, the following: * Use of strong cytochrome P450 (CYP3A) inhibitors 7 days prior to or at initiation of venetoclax, and during ramp-up phase is contraindicated in patients with MZL, CLL and MCL. For FL patients, use of strong CYP3A inhibitors is contraindicated 7 days prior to and during the first two weeks of venetoclax treatment. * Consumption of one or more of the following within 3 days prior to the first dose of any study drug: * Grapefruit or grapefruit products * Seville oranges including marmalade containing Seville oranges * Star fruit * Uncontrolled intercurrent illness including, but not limited to the following that may limit interpretation of results or that could increase risk to the patient at the discretion of the investigator: * Active hepatitis C infection. NOTE: Subjects who are hepatitis C antibody positive will need to have a negative HCV PCR result before enrollment. Those with a positive PCR for hepatitis C are excluded. * Any second malignancy that requires active systemic therapy * Known mental or physical illness that would interfere with cooperation with the requirements of the trial or confound the results or interpretation of the results of the trial and, in the opinion of the treating investigator, would make the patient inappropriate for entry into the study * Known active infection, or any major infection requiring treatment with intravenous (IV) antibiotics or hospitalization within 4 weeks prior to commencement of the study treatment. * Vaccination with a live vaccine less than or equal to 28 days prior to commencement of the study treatment. * Inability or unwillingness to swallow a large number of tablets. * Known hypersensitivity to any of the study medications or their excipients. * History of inflammatory bowel disease (e.g., Crohn's disease or ulcerative colitis). * History of malabsorption syndrome felt to be significant enough to interfere with enteral absorption at the discretion of the investigator.