Acalabrutinib With DA-EPOCH-R or R-CHOP for People With Untreated Diffuse Large B-cell Lymphoma

Background: Diffuse large B-cell lymphoma is the most common type of non-Hodgkin lymphoma. Most people with this cancer can be cured. But those who are not cured have a poor prognosis. Researchers want to add another drug to standard treatment see if it can improve the cure rate. Objective: To see if the drug acalabrutinib given with rituximab and standard combination chemotherapy can improve the cure rate of aggressive B-cell lymphomas such as diffuse large B-cell lymphoma. Eligibility: People ages 18 and older with an aggressive B-cell lymphomas that have not been treated Design: Participants will be screened with: Blood and urine tests Physical exam Medical history Tumor biopsy Bone marrow biopsy: A needle will remove marrow from the participant s hipbone. Lumbar puncture: If necessary, a needle will remove fluid from the participant s spinal canal. Imaging scans Participants will take the study drug for up to 14 days. It is a pill taken 2 times a day. Then they will have more scans. They will get rituximab and chemotherapy. They may get these drugs through a needle in an arm vein. Or they may them through a tube placed in a vein in their chest or in their neck. They might also keep taking the study drug. Each treatment cycle lasts 21 days. They will have up to 6 cycles. Participants may have 4 doses of another drug injected into their spinal fluid. Participants will have repeats of the screening tests throughout the study. Participants will have a follow-up visit 30 days after their last treatment, then every 3 months for 2 years, then every 6 months for 3 years, and then yearly.

-INCLUSION CRITERIA: 1. Patients must have a confirmed histologic diagnosis of an aggressive B-cell lymphoma with morphologic appearance of DLBCL or high-grade B-cell lymphoma (HGBL) confirmed by the Laboratory of Pathology, NCI, with no prior treatment for DLBCL or HGBL. The following subtypes are included: * DLBCL, NOS, Activated B-cell type (ABC) * DLBCL, NOS, Germinal center B-cell type (GCB) * T-cell/histiocyte-rich large B-cell lymphoma * Primary cutaneous DLBCL, leg-type * EBV+ DLBCL, NOS * DLBCL associated with chronic inflammation * ALK+ large B-cell lymphoma * High-grade B-cell lymphoma, NOS * High-grade B-cell lymphoma, with MYC and BCL2 and/or BCL6 rearrangements NOTE: Presence of concomitant indolent lymphomas such as follicular lymphoma, marginal zone lymphomas, monoclonal B-cell lymphocytosis or chronic lymphocytic leukemia/small lymphocytic lymphoma that are best categorized as composite or transformed lymphomas are allowed. 2. A formalin-fixed tissue block or 15 slide of tumor sample (archival or fresh) must be available for performance of correlative studies. NOTE: Tumor tissue may be from any previously collected tissue and adequacy is at the discretion of the Principal Investigator. Patients must be willing to have a tumor biopsy if adequate archival tissue is not available (i.e., post-enrollment and prior to treatment). 3. Measurable lymph nodes or masses of at least 1.5 centimeters (cm) on baseline CT or MRI 4. Stage II, III, or IV disease as classified by the Ann Arbor Classification 5. Age greater than or equal to 18 years 6. ECOG performance status less than or equal to 2. 7. Adequate organ and marrow function as defined below unless dysfunction is felt to be secondary to lymphoma involvement as determined by the treating investigator: * absolute neutrophil count\* \>=1,000/mcL * hemoglobin\* \>= 8 g/dL (transfusions permitted to meet criteria) * Platelets \>= 75,000/mcL (transfusions not permitted) * total bilirubin \