• 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