This study will help researchers understand how effective the combination of venetoclax and rituximab is in treating MZL in people who have not received a previous treatment for their cancer.

Inclusion Criteria:

• Age greater than or equal to 18 years

• Histologically confirmed Marginal Zone Lymphoma

• Patients must have measurable disease as defined by at least one lymph node ≥1.5 cm or spleen >13 cm.

  °Patients with intestinal MALT lymphoma must have disease that is detectable by EGD or colonoscopy with biopsy

• Patients with gastric MALT lymphoma must be h. pylori negative

  °Patients who are h. pylori positive are allowed if they have failed a trial of h.pylori eradication

• Patients with gastric MALT lymphoma who are h. pylori negative or who have relapsed/refractory disease after h. pylori eradication must be ineligible for, have refused or failed gastric radiation therapy

• ECOG performance status ≤ 1

• Life expectancy of greater than 2 years

• Patients must have normal organ function as defined below:

  • Platelet count ≥ 50,000 cells/mm^3
  • Hemoglobin ≥ 8.0 g/dL
  • Absolute neutrophil count ≥ 1000 cells/mcL. If there is documented bone marrow involvement, ANC must be >/= 500 cells/mcL
  • Total bilirubin < 1.5 x upper normal institutional limits. In patients with Gilbert's disease or documented liver involvement, total bilirubin up to 3x ULN will be allowed
  • AST(SGOT)/ALT(SGPT) <3 x institutional upper limit of normal unless elevation is caused by liver involvement with MZL

• AST(SGOT)/ALT(SGPT) <3 x institutional upper limit of normal unless elevation is caused by liver involvement with MZL

  °OR Creatinine clearance >60 mL/min for patients with creatinine levels above institutional normal (by Cockcroft-Gault estimate or 12-24h creatinine clearance measurements).

• Ability to understand and the willingness to sign a written informed consent document.

• Able to swallow pills

• HIV-positive patients on combination antiretroviral therapy are eligible if their HIV is under adequate control with an antiretroviral regimen that has been stable for > 4 weeks, as long as the CD4 count is > 300. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated.

• Patients with Hepatitis B surface antibody serum positivity due to prior immunization, as well as those with Hepatitis B core antibody positivity with negative PCR on antiviral therapy will be eligible.

Exclusion Criteria:

• Patients who have had prior systemic therapy, including rituximab

• Patients who have had prior radiation therapy, with the following exception:

  °Palliative radiotherapy RT is allowed but must be completed at least 1 week prior to treatment on this study, and prior baseline imaging studies or biopsies. Patients must meet criteria for measurable/assessable disease as outlined above after completion of RT

• Prior treatment with ibrutinib or other BTK inhibitor

• Patients with h. pylori-associated gastric MALT or stage I/II MZL will be excluded unless they are deemed to be unfit for radiation therapy with curative intent.

• Patients with uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements

  °Patients with Hep B core ab positivity are allowed provided Hep B PCR is undetectable

• Lactating or pregnant women

• Participants unwilling to adhere to institutional guidelines for highly effective contraception for 12 months after the last dose of rituximab

• Patients who received moderate or strong CYP3A inhibitors (such as fluconazole, ketoconazole, and clarithromycin) within 7 days prior to the first dose of venetoclax.

• Patients who received moderate or strong CYP3A inducers (such as rifampin, carbamazepine, phenytoin, St. John's Wort) within 7 days prior to the first dose of venetoclax.

Memorial Sloan Kettering Cancer Center supports the international committee of medical journal editors (ICMJE) and the ethical obligation of responsible sharing of data from clinical trials. The protocol summary, a statistical summary, and informed consent form will be made available on clinicaltrials.gov when required as a condition of Federal awards, other agreements supporting the research and/or as otherwise required. Requests for deidentified individual participant data can be made beginning 12 months after publication and for up to 36 months post publication. Deidentified individual participant data reported in the manuscript will be shared under the terms of a Data Use Agreement and may only be used for approved proposals. Requests may be made to: crdatashare@mskcc.org.