Pirtobrutinib in Combination With Rituximab in Adults With Untreated Marginal Zone Lymphoma (PIONEER-MZL)

Inclusion Criteria: * Subjects aged ≥ 18 years. * ECOG Performance Status ≤ 2. * Histologically confirmed marginal zone lymphoma, including splenic, nodal, and extranodal sub-types per the enrolling institution. * Subjects must have an indication for treatment. * No prior systemic therapy for MZL except for the following: * Prior antibiotic therapy for H. pylori, C. psittaci, and B. burgdorferi * Prior antiviral therapy for HCV ---Note: Subjects are eligible if they had a prior splenectomy or other local surgical treatment or local radiation therapy without systemic therapy and now require their first ever systemic therapy. In the event of the receipt of radiation therapy, the minimum washout period is 14 days * Subjects with gastric MALT lymphoma must be H. pylori negative or have failed a trial of H. pylori eradication * Subjects with localized MALT lymphoma must be ineligible for, have refused or failed radiation therapy (washout period of 14 days) * Adequate organ function as defined as: * Hematologic: * Absolute neutrophil count ≥ 750 cells/mm3 (≥ 0.75 x 10\^9/L) independent of G-CSF support, unless there is documented bone marrow involvement or splenomegaly with ensuing cytopenia in which case ANC of 500 cells/mm3 (0.5 x 10\^9/L) is permissible. Also, there should be no evidence of myelodysplasia or hypoplastic bone marrow * Platelet count ≥ 50,000/mm3 (≥50 x 10\^9/L) independent of transfusion support unless there is documented bone marrow involvement in which case platelet count of ≥30,000 cells/mm3 (≥30 x 10\^9/L) is permissible. Subjects must be responsive to transfusion support if given for thrombocytopenia and subjects refractory to transfusion support are not eligible. Also, there should be no evidence of myelodysplasia or hypoplastic bone marrow. * Note: The platelet count threshold in the current study (≥50,000 cells/mm\^3 or ≥50 x 10\^9/L) is lower than normal threshold (≥75,000 cells/mm\^3 or ≥75 x 10\^9/L) as the majority of MZL subjects have lower than normal platelets due to splenomegaly and or autoimmune phenomena (which are related to the underlying lymphoma) and hence the lower than normal platelet count threshold for study entry * Hemoglobin ≥ 8 g/dL independent of transfusion support unless there is documented bone marrow involvement or splenomegaly with ensuing cytopenia in which case hemoglobin of ≥7 g/dL (≥70 g/L) is permissible. Subjects must be responsive to transfusion support if given for anemia and subjects refractory to transfusion support are not eligible. Also, there should be no evidence of myelodysplasia or hypoplastic bone marrow. * Hepatic: ----Total Bilirubin ≤ 1.5x institutional upper limit of normal (ULN) -----Subjects with liver involvement will be allowed to enroll with total bilirubin ≤3 x ULN * AST(SGOT)/ALT(SGPT) ≤ 3 × institutional ULN ----Subjects with liver metastases will be allowed to enroll with AST and ALT levels ≤ 5 x ULN. * Renal: Estimated creatinine clearance ≥ 30 mL/min by Cockcroft-Gault formula: * aPPT or PT or INR ≤ 1.5 X ULN * Life expectancy of \>3 months, in the opinion of the investigator * For female subjects: Negative pregnancy test or evidence of post-menopausal status. The post-menopausal status will be defined as having been amenorrheic for 12 months without an alternative medical cause. The following age-specific requirements apply: * Women \< 50 years of age: ---Amenorrheic for ≥ 12 months following cessation of exogenous hormonal treatments; and * Luteinizing hormone and follicle-stimulating hormone levels in the post-menopausal range for the institution; or * Underwent surgical sterilization (bilateral oophorectomy or hysterectomy). * Women ≥ 50 years of age: * Amenorrheic for 12 months or more following cessation of all exogenous hormonal treatments; or * Had radiation-induced menopause with last menses \>1 year ago; or * Had chemotherapy-induced menopause with last menses \>1 year ago; or * Underwent surgical sterilization (bilateral oophorectomy, bilateral salpingectomy, or hysterectomy). * Female subjects of childbearing potential and male subjects with a sexual partner of childbearing potential must agree to use a highly effective method of contraception as described in Section 5.3.1. * Subjects may not plan to become pregnant or breastfeed within 1 month of the last dose of pirtobrutinib or 12 months following the last rituximab infusion * Ability to swallow oral tablets. * Subjects or their legal representatives must be able to read, understand, and provide informed consent to participate in the trial. Exclusion Criteria: * Subjects requiring therapeutic anticoagulation with warfarin or another vitamin K antagonist. * 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 * Clinically significant active malabsorption syndrome or other condition likely to affect gastrointestinal (GI) absorption of the study drug. * History of bleeding diathesis * Major surgery 4 weeks prior to starting study drug or who have not fully recovered from major surgery. * The diagnosis of another malignancy which is, in the opinion of the investigator, likely to negatively impact study participation or subject safety. * Subjects with CNS involvement * Current evidence of uncontrolled, significant intercurrent illness including, but not limited to, the following conditions: * Cardiovascular disorders: * Grade 3 NYHA functional classification system of heart failure, uncontrolled or symptomatic arrhythmias ---Unstable angina pectoris or acute coronary syndrome within 2 months of first dose. ---History of myocardial infarction within 3 months prior to the first dose of study treatment ---Stroke or intracranial hemorrhage within 6 months prior to the first dose of study treatment. * QTc prolongation defined as a QTcF \> 470 ms. ----Correction of suspected drug induced QTcF prolongation can be attempted at the investigator's discretion and only if clinically safe to do so with either discontinuation of the offending drug or switch to another drug not known to be associated with QTcF prolongation. * Correction for underlying bundle branch block (BBB) is allowed. . * Left ventricular ejection fraction \< 40% within 12 months prior to the first dose of study treatment. * Note: Subjects with pacemakers are eligible if they have no history of fainting or clinically relevant arrhythmias while using the pacemaker * Any other condition that would, in the Investigator's judgment, contraindicate the subject's participation in the clinical study due to safety concerns or compliance with clinical study procedures (e.g., infection/inflammation, intestinal obstruction, unable to swallow medication, \[subjects may not receive the drug through a feeding tube\], etc.) * Known HIV infection. * Active hepatitis B (known positive HBV surface antigen (HBsAg) result), or hepatitis C. * Note: Subjects with a past or resolved HBV infection (defined as the presence of hepatitis B core antibody \[anti-HBc\] and absence of HBsAg) are eligible, if HBV DNA PCR is negative. Subjects with positive anti-HBc and negative HBV DNA should be on prophylactic nucleo(t)side analogue therapy to prevent reactivation with serial HBV DNA PCR monitoring per section 6.6.9. Subjects positive for hepatitis C (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV RNA. * Known active cytomegalovirus (CMV) infection * Active uncontrolled auto-immune cytopenia (e.g., autoimmune hemolytic anemia \[AIHA\], idiopathic thrombocytopenic purpura \[ITP\] for which new therapy was introduced or existing therapy was escalated within the 4 weeks prior to study enrollment to maintain adequate blood counts * Medical, psychiatric, cognitive, or other conditions that may compromise the subject's ability to understand the subject information, give informed consent, comply with the study protocol or complete the study. * Known prior severe hypersensitivity to investigational product (IP) or any component in its formulations (NCI CTCAE v5.0 Grade ≥ 3).