Sonrotoclax, Rituximab, and Zanubrutinib in Treating Participants With Chronic Lymphocytic Leukemia, Small Lymphocytic Lymphoma, and Mantle Cell Lymphoma

Provision of signed and dated written informed consent prior to any study-specific procedures, sampling, or analyses

Age 18 years or older

Confirmed diagnosis (per World Health Organization \[WHO\] guidelines, unless otherwise noted) of one of the following:

* CLL/SLL COHORT: CLL/SLL diagnosis that meets the International Workshop on Chronic Lymphocytic Leukemia criteria:

* Meeting the following sets of prior treatment criteria:

* For the R/R cohort, disease that relapsed after, or was refractory to, at least 1 prior therapy

* For the treatment-naïve cohort, patients should have no prior treatment for CLL/SLL (other than 1 aborted regimen \< 2 weeks in duration and \> 4 weeks before enrollment)

* Requiring treatment per International Workshop on CLL (iwCLL) criteria

* MCL COHORT: WHO-defined MCL

* R/R MCL is defined as a disease that relapsed after, or was refractory to, at least 1 prior systemic therapy

Measurable disease, defined as:

* CLL/SLL: 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 \>= 5 x 109/L present on peripheral blood flow cytometry

* MCL, or SLL: at least 1 lymph node \> 1.5 cm in the longest diameter OR 1 extranodal lesion \> 1.0 cm in the longest diameter, measurable in 2 perpendicular dimensions by CT/MRI

Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2

Absolute neutrophil count (ANC) \>= 1.0 x 10\^9/L =\< 7 days before the first dose of the study drug with or without growth factor support. There is an exception for patients with bone marrow involvement, in which case ANC must be \>= 0.75 x 10\^9/L before the first dose of the study drug

Platelets \> 75,000 x 10\^9/L (\> 75,000 cells/mm\^3) =\< 7 days before the first dose of the study drug without the use of growth factor support or platelet transfusions. Patients with bone marrow involvement will be allowed to have a platelet count \> 50,000 x 10\^9/L (\> 50,000 cells/mm\^3) =\< 7 days before the first dose of the study drug without the use of growth factor support or platelet transfusions

Hemoglobin \> 75 g/L =\< 7 days before the first dose of the study drug (with or without transfusion)

Creatinine clearance or glomerular filtration rate (GFR) \>= 50 mL/min as estimated by one of the following:

* Cockcroft-Gault equation

* Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation

* 24-hour urine collection

Aspartate aminotransferase (AST)/serum glutamic-oxaloacetic transaminase =\< 2 x upper limit of normal (ULN)

Alanine aminotransferase (ALT)/serum glutamic-pyruvic transaminase =\< 2 x ULN

Total bilirubin level =\< 1.5 x ULN (unless documented Gilbert's syndrome). For patients with documented Gilbert's syndrome, total bilirubin may exceed this value, but direct bilirubin must be =\< 1.0 x ULN

Serum amylase =\< 1.5 x ULN

Serum lipase =\< 1.5 x ULN

Women of childbearing potential (WOCBP) must have a negative serum pregnancy test =\< 7 days before the first dose of the study drug. In addition, they must use a highly effective method of birth control initiated before the first dose of the study drug, for the duration of the study treatment period, and for \>= 180 days after the last dose of the study drug

* NOTE: WOCBP is a woman who: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (ie, has had menses at any time in the preceding 24 consecutive months)

* NOTE: Highly effective contraceptive methods include the following:

* Combined (estrogen and progestogen-containing) hormonal contraception associated with the inhibition of ovulation. Combined hormonal contraception may be oral, intravaginal, or transdermal

* Progestogen-only hormonal contraception associated with the inhibition of ovulation. Progesterone-only hormonal contraception may be oral, injectable, or implantable

* An intrauterine device

* Intrauterine hormone-releasing system

* Bilateral tubal

* Vasectomized partner

* Sexual abstinence (defined as refraining from heterosexual intercourse during the entire period of risk associated with the study treatment, starting the day before the first dose of study treatment, for the duration of the study, and for \>= 180 days after the last dose of study drug. Total sexual abstinence should only be used as a contraceptive method if it is in line with the patients' usual and preferred lifestyle. Periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods), declaration of abstinence for the duration of exposure to investigational medicinal product, and withdrawal are not acceptable methods of contraception

* Of note, barrier contraception (including male and female condoms with or without spermicide) is not considered a highly effective method of contraception, and, if used, this method must be used in combination with another acceptable method listed above

* For patients using hormonal contraceptives such as birth control pills or devices, a second barrier method of contraception (e.g., condoms) must be used

Nonsterile men must use a highly effective method of birth control along with barrier contraception for the duration of the study treatment period and for ≥ 180 days after the last dose of the study drug. During this same period, they must not donate sperm. Sterile men must use barrier contraception

Life expectancy of \> 6 months

Able to comply with the requirements of the study

* Presence of HCV antibody

Pregnant or lactating women

Unable to swallow capsules or disease significantly affecting gastrointestinal function such as malabsorption syndrome, resection of the stomach or small bowel, bariatric surgery procedure, symptomatic inflammatory bowel disease, or partial or complete bowel obstruction

Inability to comply with study procedures

Receiving any treatment with a strong or moderate CYP3A4 inhibitor =\< 14 days (or 5 half-lives, whichever is longer) before the first dose of sonrotoclax

Unwillingness to stop consumption of grapefruit, grapefruit products, Seville oranges, or starfruit within 3 days before the first dose of sonrotoclax or during the study

Receiving any treatment with a strong CYP3A4 inducer =\< 14 days (or 5 half-lives, whichever is longer) before first dose of sonrotoclax

History of interstitial lung disease, noninfectious pneumonitis, or uncontrolled lung diseases, including but not limited to pulmonary fibrosis and acute lung diseases

Autoimmune anemia and/or thrombocytopenia that is poorly controlled by corticosteroids or other standard therapy

Ongoing, drug-induced liver injury, alcoholic liver disease, nonalcoholic steatohepatitis, primary biliary cirrhosis, ongoing extrahepatic obstruction caused by cholelithiasis, cirrhosis of the liver, or portal hypertension

Receiving drugs known to prolong the QT/corrected QT (QTc) interval

Vaccination with a live vaccine =\< 35 days before the first dose of the study drug

* Note: Seasonal vaccines for influenza are generally inactivated vaccines and are allowed. Intranasal vaccines are live vaccines and are not allowed

What this study is about