Patients must meet the following criteria for study entry: 1. Histologically diagnosed marginal zone lymphoma (any subtypes) o Low grade or indolent B-cell lymphoma unclassifiable is also eligible 2. Have received at least 1 prior treatment including CD20 monoclonal antibody 3. Patients have relapsed or refractory disease to their most recent regimen 4. Stage II, III or IV disease 5. Age ≥18 years. Because no dosing or adverse event data are currently available on the use of mosunetuzumab and zanubrutinib combination in patients <18 years of age, children are excluded from this study. 6. Performance status ≤2 on the ECOG scale (≤3 if due to lymphoma) 7. Requiring systemic therapy assessed by investigator based on tumor size, symptoms and/or GELF criteria - A nodal or extranodal (except spleen) mass > 7 cm in its greater diameter - At least 3 nodal or extranodal sites ≥ 3 cm in diameter - Presence of at least one B symptom - Fever (>38 C), night sweats, weight loss > 10% in the past 6 months - Symptomatic splenomegaly (or size >13cm) - Impending organ compression or involvement (ureteral, orbital, gastrointestinal) - Any of the following cytopenias due to bone marrow involvement of lymphoma - Hemoglobin ≤ 10 g/dL - Platelets ≤ 100 x 109/L - Absolute neutrophil count (ANC) < 1.5x109/L - Pleural effusion or ascites - LDH > ULN or β2 microglobulin > ULN 8. Bi-dimensionally measurable disease, with at least one nodal lesion ≥ 1.5 cm or one extra-nodal lesion > 1 cm in longest diameter by CT, PET/CT, and/or MRI - Subjects with splenic MZL who do not meet the radiographically measurable disease criteria are eligible for participation if spleen is enlarged over 16 cm and MZL is histologically confirmed by bone marrow biopsy or peripheral blood flow cytometry - Subjects with EMZL such as skin of conjunctival EMZL who do not meet the radiographically measurable disease criteria are eligible for participation if at least one of the skin lesions is histologically confirmed as MZL and measures ≥1.5 cm in diameter 9. Patients must have adequate organ and marrow function as defined below: - Total bilirubin ≤ 1.5 institutional ULN, unless consistent with Gilbert's (ratio between total and direct bilirubin > 5) - AST (SGOT) and ALT (SGPT) ≤ 3 x institutional ULN - Alkaline phosphatase < 2.5 ULN - Creatinine clearance ≥ 40 ml/min calculated by modified Cockcroft-Gault formula - Blood counts below if without lymphoma cause for cytopenia - Hemoglobin ≥ 8 g/dL - Platelets ≥ 75 x 109/L - Absolute neutrophil count (ANC) ≥ 1.0x109/L - Blood counts below if cytopenia are due to lymphoma (such as bone marrow involvement or splenomegaly) - Hemoglobin ≥ 6 g/dL (no transfusion within 7 days prior to treatment) - Platelets ≥ 50 x 109/L - Absolute neutrophil count (ANC) ≥ 0.5x109/L

Subjects will be ineligible for this study if they meet any of following criteria: 1. Known active central nervous system lymphoma or leptomeningeal disease. 2. Treatment with any chemotherapeutic agent, or treatment with any other anti-lymphoma agent (investigational or otherwise) within 4 weeks or five half-lives of the drug, whichever is shorter, prior to first investigational agent administration. 3. Any prior history of other malignancy besides B-NHL, unless the patient has been free of disease for ≥ 1 year and felt to be at low risk for recurrence by the treating physician, except: - Adequately treated localized skin cancer without evidence of disease. - Adequately treated or monitored low risk localized prostate cancer. - Adequately treated localized breast cancer without evidence of disease. - Adequately treated cervical carcinoma in situ without evidence of disease. 4. Any life-threatening illness, medical condition, or organ system dysfunction which, in the investigator's opinion, could compromise the subject's safety, interfere with the absorption or metabolism of lenalidomide capsules, or put the study outcomes at undue risk. 5. Uncontrolled human immunodeficiency virus (HIV), or active Hepatitis C Virus, or active Hepatitis B Virus infection, or any uncontrolled active significant infection, including suspected or confirmed JC virus infection and SARS-CoV2. 6. Patients with inactive hepatitis B infection must adhere to hepatitis B reactivation prophylaxis unless contraindicated. Hepatitis B or C serologic status: subjects who are hepatitis B core antibody (anti-HBc) positive and who are surface antigen negative will need to have a negative polymerase chain reaction (PCR). Those who are hepatitis B surface antigen (HBsAg) positive or hepatitis B PCR positive will be excluded. Subjects who are hepatitis C antibody positive will need to have a negative PCR result. Those who are hepatitis C PCR positive will be excluded. Subjects with a history of Hepatitis C who received antiviral treatment are eligible as long as PCR is negative. 7. History of immunodeficiency (with the exception of hypogammaglobulinemia) or concurrent systemic immunosuppressant therapy (e.g., cyclosporine, tacrolimus, etc., or chronic administration glucocorticoid equivalent of >10mg/day of prednisone) within 28 days of the first dose of study drug with exception of steroid used for IV contrast allergy. In addition, use of inhaled, topical, intranasal corticosteroids or local steroid injection (eg, intra- articular injection) is permitted. 8. Use of strong/moderate inhibitors within 7 days or 5 half-lives prior to the first dose of zanubrutinib; usage of strong/moderate CYP3A inducers within 14 days prior to the first dose of zanubrutinib. 9. Requiring ongoing therapy with strong or moderate CYP3A inducers. 10. Clinically significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 6 months of Screening, or any Class 3 (moderate) or Class 4 (severe) cardiac disease as defined by the New York Heart Association Functional Classification. Subjects with controlled, asymptomatic atrial fibrillation during screening can enroll on study. 11. Significant screening electrocardiogram (ECG) abnormalities including 2nd degree atrioventricular (AV) block, type II AV block, or 3rd degree block. 12. Active bleeding or known bleeding diathesis (e.g., von Willebrand's disease) or hemophilia. 13. History of stroke or intracranial hemorrhage within 6 months prior to study entry. 14. Lactating or pregnant subjects. 15. Administration of any investigational agent within 28 days of first dose of study drug. 16. Patients who have undergone major surgery within 28 days or minor surgery within 3 days of first dose of study drug. 17. Patients taking corticosteroids during the last 4 weeks, unless administered at a dose equivalent to < 10 mg/day prednisone (over these 4 weeks) with the exception of pre-study steroid treatment with prednisone up to 100mg x 5 days which is allowed to improve symptoms and treatment tolerance. 18. Known or suspected chronic active Epstein-Barr virus (CAEBV) infection 19. Administration of a live, attenuated vaccine within 4 weeks before first mosunetuzumab administration or anticipation that such a live, attenuated vaccine will be required during the study. 20. Prior solid organ transplantation 21. Prior allogeneic stem cell transplant (autologous stem cell transplants are allowed if conducted at least 100 days prior to C1D1.) 22. Contraindication to tocilizumab 23. Patients who have difficulty with or are unable to swallow oral medication, or have disease significantly affecting gastrointestinal function that would limit absorption of oral medication. 24. Patients who have an active autoimmune disease that has required systemic treatment in past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is allowed. 25. Patients who have a history of (non-infectious) autoimmune pneumonitis that required steroids or has current autoimmune pneumonitis.