• Adult patients ≥18 years with histologically confirmed aggressive B-cell NHL including diffuse large B-cell lymphoma (DLBCL), either de novo or transformed from any indolent B-cell lymphoma, and including DLBCL NOS, T cell/histiocyte-rich large B-cell lymphoma, Epstein-Barr virus \[EBV\] positive DLBCL NOS, primary mediastinal \[thymic\] large B-cell lymphoma (PMBCL), high grade B-cell lymphoma NOS, or high grade B-cell lymphoma with MYC and BCL2 and/or BCL6 rearrangements \[double/triple hit lymphoma (DHL/THL)\]; and grade 3B follicular lymphoma. Patients with primary CNS lymphoma are not eligible. Patients with secondary CNS involvement by lymphoma are eligible if they otherwise meet all eligibility criteria.

• Relapsed or refractory to at least 2 prior lines of systemic lymphoma therapy. Previous therapy must have included a CD20-targeted agent and an anthracycline or alkylating agent.

• PET-positive measurable disease

• ECOG Performance status 0-2

• Estimated creatinine clearance of ≥30 mL/min, calculated using the Cockcroft and Gault equation (if male, \[140Age\] x Mass \[kg\] / \[72 x creatinine g/dL\];multiply by 0.85 if female)

• Alanine Aminotransferase (ALT) \<= 2.5 times the ULN

• Bilirubin \<= 2 x ULN (or \<= 3.0 mg/dL for patients with Gilbert-Meulengracht syndrome or lymphomatous involvement of the liver)

• Hemodynamically stable and Left Ventricle Ejection Fraction (LVEF) \>= 40% confirmed by echocardiogram or Multigated Radionuclide Angiography (MUGA)

• For subjects with atrial fibrillation, atrial fibrillation must be controlled and asymptomatic

• Absolute neutrophil count (ANC) \>= 1000/mm3

• Platelets \>= 50,000/mm3

• Adequate pulmonary function, defined as \<= CTCAE Grade 1 dyspnea and SaO2 \> 91% on room air

• Adequate vascular access for leukapheresis procedure (either peripheral line or surgically-placed line)

• Woman of childbearing potential (WOCBP) who are sexually active must use highly effective methods of contraception during treatment 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.

• Ability to understand the purpose and risks of the study and provide signed and dated informed consent and authorization to use protected health information.