BTK Inhibitor BGB-3111 in Chinese Participants With Diffuse Large B-Cell Lymphoma (Non-GCB) and Indolent Lymphoma (FL and MZL)

Key Inclusion Criteria: 1. ≥ Age 18 years at time of signing of informed consent. 2. Measurable disease by computed tomography (CT) or positron emission tomography/CT or magnetic resonance imaging, defined as ≥1 nodal lesion that was \>1.5 centimeters (cm) in the longest diameter, or ≥1 extra-nodal lesion (for example, hepatic nodules) that was \>1 cm in the longest diameter. 3. Availability of archival or fresh tumor tissue sample from an evaluable core or excisional biopsy. 4. Participants meet the following criteria: 1. Cohort 1: R/R non-GCB DLBCL i. Histologically confirmed non-GCB DLBCL per Hans criteria with non-transformed disease; additional methodologies for confirming non-GCB DLBCL may have been considered in consultation with the medical monitor. ii. Relapsed disease (disease progression after most recent therapy for DLBCL occurring more than 6 months after the completion of last therapy) or refractory disease (failure to achieve complete response \[CR\] or partial response \[PR\] to therapy for non-GCB DLBCL or disease progression within 6 months after completion of the most recent therapy for non-GCB DLBCL). iii. Must have received at least one standard anthracycline ± rituximab-based treatment (for example, rituximab plus cyclophosphamide, doxorubicin \[or epirubicin, hydroxydaunorubicin, or similar\], vincristine, and prednisone) or cyclophosphamide, vincristine, and prednisone +/- rituximab for DLBCL. 2. Cohort 2: R/R FL or R/R MZL i. Histologically confirmed CD20+ FL (Grade 1, 2, or 3a) or MZL. ii. Relapsed disease (disease progression after most recent therapy for FL or MZL occurring more than 6 months after the completion of last therapy) or refractory disease (failure to achieve complete response (CR) or partial response (PR) to most recent therapy for FL or MZL, or disease progression within 6 months after completion of the most recent therapy for FL or MZL). 5. Laboratory parameters as specified below: 1. Hematologic: Platelet count ≥75 x 10\^9/liter (L) independent of growth factor or transfusion within 7 days of study entry; absolute neutrophil count (ANC) ≥1 x 10\^9/L independent of growth factor within 7 days of study entry, hemoglobin \>8 grams/deciliter within 7 days of study entry. 2. Hepatic: Total bilirubin ≤ 2x upper limit of normal (ULN) unless documented Gilbert's syndrome; aspartate aminotransferase/serum glutamic-oxaloacetic transaminase and alanine transaminase/serum glutamic-pyruvic transaminase ≤3x ULN. 3. Renal: Creatinine clearance ≥30 milliliters/minute (as estimated by the Cockcroft-Gault equation based on ideal body weight or as measured by nuclear medicine scan or 24-hour urine collection). 4. International normalized ratio and activated partial thromboplastin time ≤1.5x ULN. Participants with anti-phospholipid syndrome, acquired von Willebrand disease, factor inhibitors or on vitamin K antagonist may have been enrolled after discussion with the Medical Monitor. 6. Left ventricular ejection fraction ≥50%. 7. Life expectancy ≥6 months. 8. Eastern Cooperative Oncology Group performance status of 0, 1, or 2. 9. Female participants of childbearing potential must have practiced highly effective methods of contraception initiated prior to first dose of study drug, for the duration of the study, and for ≥90 days after the last dose of zanubrutinib, or 12 months after the last dose of rituximab, whichever is longer. 10. Male participants were eligible if vasectomized or if they agreed to the use of barrier contraception in combination with other methods above during the study treatment period and for ≥90 days after the last dose of zanubrutinib. 11. Able to provide written informed consent and could understand and comply with the requirements of the study. Key Exclusion Criteria: 1. Known central nervous system lymphoma or leukemia. 2. Histological confirmed gastric mucosa-associated lymphoid tissue type MZL. 3. Uncontrolled autoimmune hemolytic anemia or idiopathic thrombocytopenia purpura. 4. Clinically significant cardiovascular disease. 5. History of severe bleeding disorder such as hemophilia A, hemophilia B, von Willebrand disease, or history of spontaneous bleeding requiring blood transfusion or other medical intervention. 6. History of stroke or intracranial hemorrhage within 6 months before first dose of study drug. 7. Severe or debilitating pulmonary disease. 8. Hypersensitivity reaction to zanubrutinib or rituximab or any of the other ingredients of the study drugs. 9. Prior Bruton tyrosine kinase inhibitor treatment. 10. Required ongoing treatment with a strong cytochrome P450 protein inhibitor or inducer. 11. Vaccination with a live vaccine within 28 days of the first dose of study drug. 12. Hematopoietic stem cell transplantation within 6 months of first dose of study drug. 13. Receipt of the following treatment prior to first dose of study drug: 1. Corticosteroids at doses \>20 mg/day prednisone equivalent or steroids given with anti-neoplastic intent within 7 days prior to first dose of study drug. 2. Chemotherapy or radiotherapy within 4 weeks. 3. Monoclonal antibody within 4 weeks. 4. Investigational therapy within 4 weeks. 5. Chinese patent medicine with anti-neoplastic intent within 4 weeks. 14. Not recovered from toxicity of any prior anti-cancer therapy to ≤Grade 1, except for alopecia, ANC, hemoglobin (Hgb), and platelets. For ANC, Hgb and platelets, see inclusion criterion #5. 15. Prior malignancy within the past 3 years, except for curatively treated basal or squamous cell skin cancer, superficial bladder cancer, or carcinoma in situ of the cervix or breast. 16. Unable to swallow capsules or disease significantly affecting gastrointestinal function such as malabsorption syndrome, resection of the stomach or small bowel, symptomatic inflammatory bowel disease, history of bariatric surgery, or partial or complete bowel obstruction. 17. Major surgery within 4 weeks prior to first dose of study treatment. 18. Active fungal, bacterial and/or viral infection requiring systemic therapy. 19. Known infection with human immunodeficiency virus, or serologic status reflecting active hepatitis B or C infection as follows: 1. Presence of hepatitis B surface antigen (HBsAg) or anti-hepatitis B core antibody (anti-HBc). Participants with presence of anti-HBc, but absence of HBsAg, were eligible if hepatitis B virus (HBV) DNA was \<500 international units (IU)/mL, anti-viral therapy started before the first dose of study treatment, and if they were willing to undergo monthly monitoring for HBV reactivation. 2. Presence of hepatitis C virus (HCV) antibody. Participants with presence of HCV antibody were eligible if HCV RNA was undetectable (\<15 IU/mL). 20. Pregnant or lactating women. 21. Underlying medical conditions that, in the investigator's opinion, would have rendered the administration of study drug hazardous or obscure the interpretation of toxicity or adverse events. 22. Concurrent participation in another therapeutic clinical trial. Note: Other protocol defined Inclusion/Exclusion criteria may have applied.