Acalabrutinib Maintenance Following Cellular Therapy for Large B-Cell Lymphoma Patients at Very High Risk for Relapse

Inclusion Criteria: * Ages 18-70 years * One of the following: * Patients undergoing autologous stem cell transplantation (ASCT) or any Food and Drug Administration (FDA)-approved chimeric antigen receptor (CAR) T-cell therapy product for: * High grade B-cell lymphoma (double or triple hit) with rearrangements in bcl-2 and/or bcl-6, and rearrangement in myc * Large B-cell lymphoma with a history of secondary CNS involvement * Histologic transformation of indolent lymphoma to large B-cell lymphoma, including marginal zone lymphoma, follicular lymphoma, chronic lymphocytic leukemia (CLL), small lymphocytic lymphoma (SLL), lymphoplasmacytic leukemia, or Waldenstrom macroglobulinemia * High risk international prognostic index (IPI) score 4 or 5, at diagnosis or prior to CAR T-cell leukapheresis * Patients undergoing allogeneic hematopoietic cell transplantation (alloHCT) for large B-cell lymphoma * Eastern Cooperative Oncology Group (ECOG) 0-2 * Requirements for post-ASCT and post-alloHCT participants: * Disease status of partial response (PR) or complete response (CR) prior to transplantation * Receive reduced-intensity conditioning regimen * Enrollment no later than day +90 * Requirements for post-CAR T-cell therapy participants: * Disease status of PR or CR after post-CAR T-cell therapy positron emission tomography (PET)-computed tomography (CT) at 1-3 months * Enrollment no later than day +104 * Ability to give full informed consent * Female subjects who are sexually active and can bear children must agree to use highly effective forms of contraception while on the study and for 2 days after the last dose of acalabrutinib * Willing and able to participate in all required evaluations and procedures in this study protocol, including swallowing capsules and tablets without difficulty * Absolute neutrophil count (ANC) \> 500/uL (microliters) * Platelets \> 50,000/uL independent of transfusions * Hemoglobin \> 8 g/dL independent of transfusions * Serum aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3 x upper limit of normal (ULN) * Total bilirubin =\< 1.5 x ULN, unless directly attributable to Gilbert's syndrome * Creatinine clearance \>= 60 mL/min based on Cockcroft-Gault glomerular filtration rate (GFR) and serum creatinine (Cr) =\< 1.8 mg/dL Exclusion Criteria: * Cord blood as donor source in alloHCT * New York Heart Association Class III or IV * Left ventricular ejection fraction \< 50% * Estimated glomerular filtration rate \< 30 mL/min * Concurrent long-term use of posaconazole or other strong CYP3A4 inhibitors and unable to replace with equivalent medication * Acute or chronic graft-versus-host disease (GvHD) \>= stage 3 at time of enrollment * Received packed red blood cells (pRBC) transfusion within the past 2 weeks * Received platelet transfusion within the past 1 week * Active invasive fungal infection * Active bacterial or viral infection until resolution of the infection * History of or ongoing confirmed progressive multifocal leukoencephalopathy (PML) * Received any investigational drug within 30 days or 5 half-lives (whichever is shorter) before first dose of study drug * Major surgical procedure within 30 days before the first dose of study drug. Note: If a subject had major surgery, they must have recovered adequately from any toxicity and/or complications from the intervention before the first dose of study drug * Refractory nausea and vomiting, inability to swallow the formulated product, or malabsorption syndrome; chronic gastrointestinal disease, gastric restrictions, or bariatric surgery such as gastric bypass; partial or complete bowel obstruction, or previous significant bowel resection that would preclude adequate absorption, distribution, metabolism, or excretion of study treatment * Received a live virus vaccination within 28 days of first dose of study drug * Known history of infection with human immunodeficiency virus (HIV) * History of bleeding diathesis (e.g., hemophilia, von Willebrand disease) * Requires or receiving anticoagulation with warfarin or equivalent vitamin K antagonists * Requires treatment with a strong cytochrome P450 3A (CYP3A) inhibitor or inducer. The use of strong CYP3A inhibitors within 1 week or strong CYP3A inducers within 3 weeks of the first dose of study drug is prohibited * Breastfeeding or pregnant * Concurrent participation in another therapeutic clinical trial