Rituximab Plus Venetoclax in Front Line Marginal Zone Lymphoma

Inclusion Criteria: * Participants must have 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 relapsed/refractory disease after h. pylori eradication must be ineligible form have refused or failed gastric radiation therapy * Age ≥18 years * ECOG performance status ≤1 * Life expectancy of greater than 2 years * Participants must meet the following organ and marrow function as defined below: * Hemoglobin ≥8.0 g/dL * absolute neutrophil count ≥1,000 cells/mcL (In the event of documented bone marrow involvement, ANC must be ≥1500 cells/mcL) * platelets ≥50,000 cells/mm3 * total bilirubin \< 1.5 x institutional upper limit of normal (ULN) (In patients with Gilberts disease or documented liver involvement, total bilirubin \< 3 X ULN will be allowed) * AST(SGOT)/ALT(SGPT) \< 3 × institutional ULN unless elevation is caused by liver involvement with MZL * Creatinine within institutional ULN OR creatinine clearance \>60mL/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 * Patient must be 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 poor immunization, as well as those with Hepatitis B core antibody positivity with negative PCR on antiviral therapy will be eligible Exclusion Criteria: * Patients who had prior systemic therapy including rituximab * Patients who have had prior radiation therapy, with the following exceptions: * Palliative radiotherapy (RT) is allowed, but must be completed at least 1 week prior to treatment on this study, and prior to any baseline imaging studies or biopsies. Patients must meet criteria for measurable/assessable disease as outlined above after completion of RT. * Prior RT for gastric MALT is allowed, but must be completed at least 1 week prior to treatment on this study, and prior to any 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. * 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 uncontrolled hepatitis B or C or HIV infection are ineligible defined as patients with positive serologies and a detectable viral load by PCR. * Patients with Hep B core ab positivity are allowed provided Hep B PCR is undetectable * Pregnant women or participants unwilling to adhere to institutional guidelines for highly effective contraception for 12 months after the last dose of rituximab are excluded from this study because of documented risks of rituximab on fetal immunologic development and unknown effects of venetoclax on embryonic development. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with venetoclax, breastfeeding should be discontinued. * Received moderate or strong CYP3A inhibitors (such as fluconazole, ketoconazole, and clarithromycin) within 7 days prior to the first dose of venetoclax. * 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.