Zanubrutinib in Combination With Sonrotoclax for the Treatment of Underrepresented Ethnic and Racial Minorities With Relapsed or Refractory B-cell Non-Hodgkin Lymphoma

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * Age: ≥ 18 years on the day of signing the informed consent form * Eastern Cooperative Oncology Group (ECOG) ≤ 2 * Patients are of the following self-identified racial/ethnic groups: * Cohort 1: Patients in any of the following categories: * Black or African American * Hispanic or Latino * American Indian/Native Alaskan * Pacific Islander/Native Hawaiian * Any other patient that does not fit the definition of Cohort 2 * Cohort 2: Patients in either of following categories: * Non-Hispanic White * Non-Hispanic Asian * Confirmed diagnosis (per World Health Organization \[WHO\] guidelines, unless otherwise noted) of one of the following disease subtypes. Note that for disease subtypes that are known to respond to BTK inhibitor (BTKi) and/or BCL2 inhibitor (BCL2i) (e.g., marginal zone lymphoma \[MZL\], mantle cell lymphoma \[MCL\], CLL/SLL), newly diagnosed or r/r patients are allowed * Diffuse large B cell lymphoma (DLBCL) * R/R DLBCL (including all subtypes of DLBCL) defined as disease that relapsed after, or was refractory to, at least 2 prior lines of therapy. Patients should be considered by the investigator to be refractory to or not a candidate for approved therapies with proven efficacy including but not limited to chimeric antigen receptor (CAR) T cell therapy or bispecific antibody therapy * Active disease requiring treatment * Follicular lymphoma (FL) * R/R FL (grade 1, 2 or 3a based on WHO 2008 classification of tumors of hematopoietic and lymphoid tissue) and defined as disease that relapsed after, or was refractory to, at least 1 prior systemic therapy. Patients should be considered by the investigator for all approved therapies with proven efficacy including but not limited to CAR T cell therapy or bispecific antibody therapy * Active disease requiring treatment * Marginal zone lymphoma (MZL) * R/R extranodal, splenic, or nodal MZL defined as disease that relapsed after, or was refractory to, at least 1 prior therapy * Active disease requiring treatment * Mantle cell lymphoma (MCL) * R/R MCL defined as disease that relapsed after, or was refractory to, at least 1 prior systemic therapy * Requiring treatment in the opinion of the investigator * Chronic lymphocytic leukemia/small lymphocytic leukemia (CLL/SLL) * CLL/SLL diagnosis that meets the International Workshop on CLL (International Workshop on Chronic Lymphocytic Leukemia \[IWCLL\]) criteria * Patients with previously untreated and/or r/r CLL defined as disease that relapsed after, or was refractory to, at least 1 prior therapy will be included * Patients must have an indication to start treatment * Measurable disease, defined as: * CLL: at least 1 lymph node \> 1.5 cm in longest diameter and measurable in 2 perpendicular dimensions by computed tomography (CT)/magnetic resonance imaging (MRI) or clonal lymphocytes measured by flow cytometry * DLBCL, FL, MZL, MCL, or SLL: at least 1 lymph node \> 1.5 cm in longest diameter OR 1 extranodal lesion \> 1.0 cm in the longest diameter, measurable in 2 perpendicular dimensions by CT/MRI. For MZL, isolated splenomegaly is considered measurable for this study. For MCL, clonal lymphocytes measured by flow cytometry is considered measurable * Life expectancy of ≥ 6 months * Without bone marrow involvement: Absolute neutrophil count (ANC) ≥ 1,000/mm\^3 * NOTE: Growth factor is not permitted within 7 days of ANC assessment unless cytopenia is secondary to disease involvement * With bone marrow involvement: ANC ≥ 500/mm\^3 * NOTE: Growth factor is not permitted within 7 days of ANC assessment unless cytopenia is secondary to disease involvement * Without bone marrow involvement: Platelets ≥ 75,000/mm\^3 * NOTE: Platelet transfusions are not permitted within 7 days of platelet assessment unless cytopenia is secondary to disease involvement * With bone marrow involvement: Platelets ≥ 30,000/mm\^3 * NOTE: Platelet transfusions are not permitted within 7 days of platelet assessment unless cytopenia is secondary to disease involvement * Hemoglobin ≥ 7g/dL * NOTE: Red blood cell transfusions are not permitted within 7 days of hemoglobin assessment unless cytopenia is secondary to disease involvement * Total bilirubin ≤ 1.5 x upper limit of normal (ULN) (unless has Gilbert's disease) * Aspartate aminotransferase (AST) ≤ 2.5 x ULN * Alanine aminotransferase (ALT) ≤ 2.5 x ULN * Creatinine clearance of ≥ 30 mL/min per 24 hour urine test or the Cockcroft-Gault formula * Fridericia's formula-corrected QT interval (QTcF) ≤ 480 ms * Note: Performed within 28 days prior to day 1 of protocol therapy * Seronegative for HIV antigen (Ag)/antibody (Ab) combo, hepatitis C virus (HCV), active hepatitis B virus (HBV) (surface antigen negative) OR * If seropositive for HIV, HCV or HBV, nucleic acid quantitation must be performed. Viral load must be undetectable * HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial * Meets other institutional and federal requirements for infectious disease titer requirements * Note Infectious disease testing to be performed within 28 days prior to day 1 of protocol therapy * Women of childbearing potential (WOCBP): Negative urine or serum pregnancy test * If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Agreement by females and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 90 days after the last dose of protocol therapy * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) Exclusion Criteria: * Major surgery ≤ 4 weeks of the first dose of study drug * Prior autologous stem cell transplant unless ≥ 30 days after transplant; or prior chimeric antigen receptor T cell (CAR-T) therapy unless ≥ 30 days after cell infusion * Prior allogeneic stem cell transplant with active graft-versus-host disease (GVHD), or requiring immunosuppressive drugs for treatment of GVHD, or have taken calcineurin inhibitors within 4 weeks prior to consent * Prior therapy ≥ 2 months with or progression on a Bcl2 inhibitor (eg, venetoclax) * Vaccination or requirement for vaccination with a live vaccine within 35 days prior to the first dose of study drug or at any time during planned study treatment * Requires ongoing treatment with a strong CYP3A inducer * Requires ongoing treatment with warfarin or warfarin derivatives * Concurrent participation in another therapeutic clinical trial * Use of the following substances prior to the first dose of study drug: * ≤ 28 days before first dose of study drug: Any biologic and/or immunologic-based therapy(ies) including experimental therapy(ies) for leukemia, lymphoma, or myeloma (including, but not limited to, monoclonal antibody therapy, eg, rituximab, and/or cancer vaccine therapy) * ≤ 14 days before the first dose of study drug: systemic chemotherapy or radiation therapy * ≤ 7 days before the first dose of study drug: corticosteroid given with antineoplastic intent other than control of BTK inhibitor withdrawal flare * ≤ 5 half-lives before the first dose of study drug: BTK inhibitor, tyrosine kinase inhibitor, or other targeted small molecule given with antineoplastic intent * Known current central nervous system involvement by lymphoma/leukemia * Known plasma cell neoplasm, prolymphocytic leukemia, history of or currently suspected Richter's syndrome * Any uncontrolled or clinically significant cardiovascular disease including the following: * Myocardial infarction (MI) within 6 months before screening * NYHA (New York Heart Association) heart failure class III-IV * Unstable angina within 3 months before screening * History of clinically significant arrhythmias (e.g., sustained ventricular tachycardia, ventricular fibrillation, torsades de pointes) * History of Mobitz II second-degree or third-degree heart block without a permanent pacemaker in place * Prior malignancy within the past 3 years, except for curatively treated basal or squamous cell skin cancer, non-muscle-invasive bladder cancer, carcinoma in situ of the cervix or breast, or localized Gleason score 6 prostate cancer * 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 * History of stroke or intracranial hemorrhage within 6 months before first dose of study drug * Severe or debilitating pulmonary disease * Unable to swallow capsules or disease significantly affecting gastrointestinal function such as malabsorption syndrome, resection of the stomach or small bowel, bariatric surgery procedures, symptomatic inflammatory bowel disease, or partial or complete bowel obstruction * Active fungal, bacterial and/or viral infection requiring systemic therapy * Underlying medical conditions that, in the investigator's opinion, will render the administration of study drugs hazardous or obscure the interpretation of toxicity or adverse events (AEs) * Known active infection with HIV, or serologic status reflecting active hepatitis B or C infection as follows: * Presence of hepatitis B surface antigen (HBsAg) or hepatitis B core antibody (HBcAb). Patients with presence of HBcAb, but absence of HBsAg, are eligible if hepatitis B virus (HBV) deoxyribonucleic acid (DNA) is undetectable (\< 20 IU), and if they are willing to undergo monitoring every 4 weeks for HBV reactivation * Presence of hepatitis C virus (HCV) antibody. Patients with presence of HCV antibody are eligible if HCV ribonucleic acid (RNA) is undetectable * Any condition which in the discretion of the investigator would compromise the ability to comply with study procedures * History of allergic reactions attributed to compounds of similar chemical or biologic composition to the study agents * Active and/or ongoing autoimmune anemia and/or autoimmune thrombocytopenia (e.g., idiopathic thrombocytopenia purpura) * Females only: Pregnant or breastfeeding * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)