• Diagnosis of RS - occurrence of diffuse large B-cell lymphoma (DLBCL) in patients with antecedent or concurrent CLL/SLL (CLL/SLL diagnosis per IWCLL 2018 criteria).

• Must have relapsed/refractory disease as defined by one of the following:

‣ Participants must have undergone \>= 1 prior systemic therapeutic regimen administered for \>= 1 cycle for either CLL or RS, and have had either documented disease progression to the most recent treatment regimen, or refractory disease. OR

⁃ Developed RS while receiving treatment for CLL

• Age \>= 18 years

• Eastern Cooperative Oncology Group (ECOG) performance status =\< 2

• Total bilirubin =\< 2.0 times the institutional upper limit of normal (unless documented Gilbert's syndrome)

• Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) =\< 2.5 x institutional upper limit of normal

• Alanine aminotransferase (ALT) (serum glutamic-pyruvic transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal

• Creatinine clearance \>= 30 mL/min

‣ Using 24-hour creatinine clearance or standard Cockcroft-Gault equation

• Absolute lymphocyte count \> 100/uL at screening

• Left ventricular ejection fraction \>= 40% by multigated acquisition (MUGA) or echocardiogram (ECHO)

• Adequate bone marrow independent of growth factor support or infusion support at screening unless evidence shows that the cytopenia(s) is due to marrow involvement by CLL/small lymphocytic lymphoma (SLL). If cytopenias are due to disease in the bone marrow any degree of anemia or thrombocytopenia are allowed, absolute neutrophil count (ANC) must be \>= 500

• Absolute neutrophil count (ANC) \>= 1000/mm\^3 (independent of growth factor support or infusion support at screening unless evidence shows that the cytopenia\[s\] is due to marrow involvement by CLL/SLL). If cytopenias are due to disease in the bone marrow any degree of anemia or thrombocytopenia are allowed, ANC must be \>= 500

• Platelets \>= 30,000/mm\^3 (independent of growth factor support or infusion support at screening unless evidence shows that the cytopenia\[s\] is due to marrow involvement by CLL/SLL). If cytopenias are due to disease in the bone marrow any degree of anemia or thrombocytopenia are allowed

• Hemoglobin \>= 7 g/dL (independent of growth factor support or infusion support at screening unless evidence shows that the cytopenia\[s\] is due to marrow involvement by CLL/SLL). If cytopenias are due to disease in the bone marrow any degree of anemia or thrombocytopenia are allowed

• Radiographically measurable lymphadenopathy (or measurable extra-nodal disease) per Lugano criteria

• Must meet all institutional standards for receiving CAR T-cell therapy

• Subjects (or legal guardians) must have the ability to understand and the willingness to sign a written informed consent document

• For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use a contraceptive method with a failure rate of \< 1% per year, initiated prior to first dose of study drug, during the treatment period and for at least 1 year after the CAR-T cell infusion or 1 month after last dose of zanubrutinib, whichever is longer.

‣ A woman is considered to be of childbearing potential if she is postmenarcheal, has not reached a postmenopausal state (\< 12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (removal of ovaries and/or uterus). Examples of contraceptive methods with a failure rate of \< 1% per year include bilateral tubal ligation, male sterilization, hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices

• For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures, and agreement to refrain from donating sperm, as defined below:

‣ With female partners of childbearing potential, men must remain abstinent or use a condom plus an additional contraceptive method that together result in a failure rate of \< 1% per year during the treatment period and for at least 1 year after the anti-CD19 CAR-T cell infusion or 1 month after last dose of zanubrutinib, whichever is longer. Men should avoid fathering a child and refrain from donating sperm during this same period.

⁃ With pregnant female partners, men must remain abstinent or use a condom during the treatment period and for at least 1 year after the human anti- CD19 CAR-T cell infusion or 1 month post last dose of zanubrutinib, whichever is longer, to avoid potential embryonal or fetal exposure. The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not acceptable methods of contraception