• 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)