Inclusion Criteria:  Patients must have a histo-pathologically confirmed diagnosis of an aggressive B-cell non-Hodgkin lymphoma or transformed indolent B-cell lymphoma that is recurrent or refractory to standard therapy and with intent to treat with standard of care CAR T-cell therapy (meeting Food and Drug Administration [FDA] approved indications for the respective CAR T-cell construct being used). Standard of care /FDA approved CARTs for this population include axicabtagene ciloleucel, tisagenlecleucel or lisocabtagene maraleucel, any of which may be used for this study and provider dependent. For the purpose of this study, aggressive B-cell NHL histologies should conform to the label indications for the respective CART being utilized. Accordingly, CART eligible histologies include the following groups according to the 2016 revision of the World Health Organization (WHO) classification of lymphoid neoplasms  High-grade B-cell lymphoma, with MYC and BCL2 and/or BCL6 rearrangements High-grade B-cell lymphoma, not otherwise specified (NOS) Diffuse large B-cell lymphoma (DLBCL), NOS Diffuse large B-cell lymphoma (DLBCL), NOS; Germinal center B-cell type Diffuse large B-cell lymphoma (DLBCL), NOS; Activated B-cell type Large B-cell lymphoma with IRF4 rearrangement T-cell/histiocyte-rich large B-cell lymphoma (subtype of DLCBL) Primary cutaneous DLBCL, leg type (subtype of DLCBL) Epstein-Barr virus (EBV)+ DLBCL, NOS (subtype of DLCBL) DLBCL associated with chronic inflammation (subtype of DLCBL) Primary mediastinal (thymic) large B-cell lymphoma Intravascular large B-cell lymphoma (subtype of DLCBL) Transformed indolent B-cell lymphoma; composite lymphomas with aggressive B-cell NHL as outlined above and indolent lymphomas are also allowable if felt to represent transformation Patients should have measurable disease per Lugano criteria (2014) Patients must be age >= 18 years Patients must exhibit an Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 Patients must have a life expectancy of greater than 12 weeks Females of childbearing potential must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin [HCG]) within 28 days prior to registration Absolute neutrophil count (ANC) >= 500/uL neutrophil count (within 14 days of registration)  Platelets (PLT) >= 50,000/uL (within 14 days of registration)  NOTE: Red blood cell (RBC) and platelet transfusion allowed >= 7 days prior to registration Total bilirubin =< 1.5 x institutional upper limit of normal (ULN) (except patients with Gilbert syndrome, who can have total bilirubin < 3.0 mg/dL) (within 14 days of registration) Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5 x institutional ULN (within 14 days of registration) Creatinine clearance >= 30 mL/min estimated by the Cockcroft-Gault equation (within 14 days of registration)  Patients with evidence of hepatitis B virus (HBV) are eligible provided there is minimal hepatic injury and the patient has undetectable HBV on suppressive HBV therapy  Note: Patient must be willing to maintain adherence to HBV therapy. Patients with previously treated and eradicated hepatitis C virus (HCV) who have minimal hepatic injury are eligible  The effects of zanubrutinib on the developing human fetus are unknown. For this reason and because other therapeutic agents used in this trial are known to be teratogenic, females of child-bearing potential (FOCBP) and men must agree to use highly effective contraception (hormonal or ; complete abstinence) from time of informed consent, for the duration of study participation, and for 180 days following completion of therapy  NOTE: A FOCBP is any woman (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) who meets the following criteria:  Has not undergone a hysterectomy or bilateral oophorectomy Has had menses at any time in the preceding 12 consecutive months (and therefore has not been naturally postmenopausal for > 12 months)  FOCBP must agree to practice 1 highly effective methods of contraception and 1 additional effective (barrier) method, at the same time. Otherwise females should  Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the patient. (Periodic abstinence [e.g., calendar, ovulation, symptothermal, post ovulation methods], withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception.) Females should also agree to not donate eggs (ova) during the course of this study or 180 days after receiving their last dose of study drug. Should a female patient become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately  Men treated or enrolled on this protocol must also agree to use adequate contraception from time of informed consent, for the duration of study participation, and 180 days after completion of administration. Men even if surgically sterilized (i.e., status post-vasectomy) must agree to 1 of the following:  Agree to practice highly effective barrier contraception during the entire study treatment period and through 180 days after the last dose of study drug, OR Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the patient. (Periodic abstinence [e.g., calendar, ovulation, symptothermal, post ovulation methods for the female partner], withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception.)  Agree not to donate sperm during the course of this study or 180 days after receiving their last dose of study drug.  Note: Female and male condoms should not be used together Ability to understand and the willingness to sign a written informed consent document  Exclusion Criteria:  Patients who are receiving any other investigational agents are not eligible Patients who require treatment with moderate or strong CYP3A inducers =< 7 days prior to treatment with zanubrutinib lead-in are not eligible  Patients requiring systemic treatment with corticosteroids (> 10mg daily prednisone equivalents) or other immunosuppressive medications including anti-neoplastic therapies =< 7 days prior to treatment with zanubrutinib lead-in are not eligible  Please note: Steroids for treatment of lymphoma and/or management of CAR T-cell toxicities are allowed from time of apheresis until 90 days post CAR T-cell therapy. In the event that steroids are deemed necessary for CAR T-cell toxicities after 90 days, this may be done upon discussion with the principal investigator (PI) Patients with evidence of active disease in the central nervous system (CNS) defined as either the presence of active lesions on magnetic resonance imaging (MRI) obtained within 4 weeks prior to registration or progressive neurological decline are not eligible  Patients are not eligible if they have uncontrolled intercurrent illness including, but not limited to  Ongoing or active infection Symptomatic congestive heart failure Unstable angina pectoris Cardiac arrhythmia deemed clinically significant by the provider Or psychiatric illness/social situations that would limit compliance with study requirements Pregnant women and nursing mothers are not eligible Patients with human immunodeficiency virus (HIV) are not eligible Patients who are unable to swallow oral tablet/gel capsules are not eligible Patients who have gastrointestinal disorders or abnormalities that would interfere with absorption of the study drug are not eligible