-  INCLUSION CRITERIA:

          -  Patients must have a confirmed histologic diagnosis of an indolent 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, 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 lymphoma (CLL)

          -  Relapsed and/or refractory disease that has failed at least two (2) prior lines of
             therapy with at least one of those therapies containing an anti-CD20 monoclonal
             antibody. Patients must not have received prior treatment with a CD47 or SIRP alpha
             targeting agent.

        NOTE: Patients with CLL are not required to have had therapy containing anti-CD20.

        -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 CT or MRI and/or evaluable FDG-avid
        lesions on PET). Patients may also have measurable disease.

        NOTE: Patients with known active 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

          -  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 9.5 g/dL (transfusions permitted). NOTE:
                  Patients must have required fewer than 2 units of 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 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 (SqrRoot) ULN

        NOTE: Patients with Gilbert's syndrome may have a bilirubin level > 1.5 (SqrRoot) 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: 120 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 DNA PCR positive. NOTE: Subjects who are
             hepatitis B core antibody positive will need to have a negative 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 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 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.