Zanubrutinib and Lisocabtagene Maraleucel for the Treatment of Richter's Syndrome

Inclusion Criteria: * 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 Exclusion Criteria: * A history of treatment including any of the following: prior CD19 directed therapy, treatment with alemtuzumab within 6 months before enrollment, prior allogeneic hematopoietic stem cell transplant (SCT) or donor lymphocyte infusion (DLI) within 2 months prior to enrollment * 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 * Inadequate recovery from adverse events related to prior therapy to grade =\< 1 (excluding grade 2 alopecia, neuropathy, and hypertension) * Is unable to swallow oral medication, or has significant gastrointestinal disease that would limit absorption of oral medication * Active bleeding or history of bleeding diathesis (e.g., hemophilia or von Willebrand disease) * Uncontrolled autoimmune hemolytic anemia (AIHA) or idiopathic thrombocytopenic purpura (ITP) * Presence of a gastrointestinal ulcer diagnosed by endoscopy within 3 months before screening * Clinically significant cardiovascular disease such as symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 6 months of screening, or any class 3 or 4 cardiac disease as defined by the New York Heart Association Functional Classification. Note: Subjects with controlled atrial fibrillation/flutter can enroll on study * Requires or receiving anticoagulation with warfarin or equivalent vitamin K antagonists * Prothrombin time (PT)/international normalized ratio (INR) or activated partial thromboplastin time (PTT) (in the absence of lupus anticoagulant) \> 2 x upper limit normal (ULN) * Treatment with a moderate or strong CYP3A inhibitor or inducer within 7 days prior to first dose of zanubrutinib * Patients may not have an active intercurrent disease or concurrent malignancy that is expected to limit survival to \< 5 years * Human immunodeficiency virus (HIV) seropositivity at screening * Subjects with uncontrolled intercurrent illness including, but not limited to ongoing or active infection, unstable angina pectoris, pulmonary abnormalities or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant or breastfeeding women are excluded from this study because CAR-T cell therapy may be associated with the potential for teratogenic or abortifacient effects. Women of childbearing potential must have a negative serum pregnancy test. Because there is an unknown, but potential risk for adverse events in nursing infants secondary to treatment of the mother with CAR-T cells, breastfeeding should be discontinued. These potential risks may also apply to other agents used in this study * Evidence of myelodysplasia or cytogenetic abnormality indicative of myelodysplasia on any bone marrow biopsy prior to initiation of therapy * Serologic status reflecting active hepatitis B or C infection at screening. Patients that are positive for hepatitis B core antibody, hepatitis B surface antigen (HBsAg), or hepatitis C antibody must have a negative polymerase chain reaction (PCR) at screening. PCR positive patients will be excluded * History of autoimmune disease (i.e. rheumatoid arthritis, systemic lupus erythematosus) with requirement of immunosuppressive medication within 6 months * Chronic use of corticosteroids \>= 20mg prednisone equivalent PO daily * Live vaccines given in 28 days prior to lymphodepleting chemotherapy