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

-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 \<= 1.5 X institutional ULN (or \<= 3 X institutional ULN for patients with documented Gilberts syndrome or cholestatic obstruction or involvement by lymphoma) * AST(SGOT)/ALT(SGPT) \<= 3 X institutional ULN (\<= 5 x ULN for patients with cholestatic obstruction or involvement by lymphoma * Serum creatinine \<= 2.0 mg/dL OR -Creatinine clearance \>=40 mL/min/1.73 m2 for patients with creatinine levels above 2 mg/dL \*RBC transfusions and use of G-CSF will be allowed in order to meet eligibility parameters. NOTE: In patients without bone marrow involvement, transfusions of RBCs are permitted to achieve the criterion hemoglobin of 8g/dl, but transfusions of platelets are not permitted to achieve the criterion platelet count of \>75,000/mcL. In patients with bone marrow involvement, all transfusions are permissible at the discretion of the investigator. 8. Effects of acalabrutinib on the developing human fetus are unknown. For these reasons the following measures apply: * Individuals of childbearing potential must have a negative serum or urine pregnancy test within 7 days prior to enrollment. * Individuals of childbearing potential who are sexually active must agree to highly effective contraception prior to study entry, for the duration of study participation, and for at least 2 days after the last dose of acalabrutinib or 12 months after the last dose of combined chemotherapy, whichever is later. Individuals who can father children must use highly effective contraception prior to study entry, for the duration of study participation, and for 12 months after the last dose of combined chemotherapy; there is no contraception timing requirement post-last dose of acalabrutinib alone if an individual who can father children does not initiate chemotherapy on study after the acalabrutinib window. * Participants must not be planning to conceive or father children within the projected duration of the trial, starting with the pre-screening/screening visit through 2 days after the last dose of acalabrutinib or 12 months after the last dose of combined chemotherapy, whichever is later. NOTE: An individual is considered of childbearing potential, (i.e., fertile), following menarche and until becoming post-menopausal unless permanently sterile or have a congenital or acquired condition that prevents childbearing. Permanent sterilization methods include but are not limited to hysterectomy, bilateral salpingectomy and bilateral oophorectomy at least 6 weeks before screening. A postmenopausal state is defined as no menses for continuous 12 months without an alternative medical cause. In individuals of childbearing potential \<45 years of age, a high follicle stimulating hormone (FSH) level in the postmenopausal range may be used to confirm a post-menopausal state in individuals of childbearing potential not using hormonal contraception or hormonal replacement therapy. In the absence of 12 months of amenorrhea, a single FSH measurement is insufficient The investigator or a designated associate is requested to advise the subject how to achieve highly effective birth control (failure rate of less than 1%), e.g., intrauterine device (IUD), intrauterine hormone-releasing system (IUS), bilateral tubal occlusion, vasectomized partner and sexual abstinence. Individuals who can father children are considered to be of non-reproductive potential if they are permanently sterile due to bilateral orchiectomy. Highly effective methods of contraception (to be used during heterosexual activity) are defined as methods that can achieve a failure rate of \<1% per year when used consistently and correctly. Such methods include: * Combined (estrogen and progestogen containing) hormonal contraception associated with inhibition of ovulation, which may be oral, intravaginal, or transdermal * Progestogen-only hormonal contraception associated with inhibition of ovulation, which may be oral, injectable, or implantable * Intrauterine device (IUD) or intrauterine hormone-releasing system (IUS) * Bilateral tubal occlusion * Vasectomy of participant or participant's partner (with medical assessment and confirmation of vasectomy surgical success) * Sexual abstinence (only if refraining from heterosexual intercourse during the entire period of risk associated with the study treatments) Hormonal contraception may be susceptible to interaction with study or other drugs, which may reduce the efficacy of the contraception method. Abstinence (relative to heterosexual activity) can only be used as the sole method of contraception if it is consistently employed during the entire period of risk associated with the study treatments. Periodic abstinence (e.g., calendar, ovulation, sympto-thermal, and post-ovulation methods) and withdrawal are not acceptable methods of contraception. 9. Ability of patient to understand and the willingness to sign a written informed consent document. 10. Any HIV status will be included in this study; status must be confirmed prior to enrollment. EXCLUSION CRITERIA: 1. Patients who meet histologic criteria for the following subtypes are excluded: * Primary DLBCL of the central nervous system (PCNSL) * Primary mediastinal B-cell lymphoma (PMBL) * Plasmablastic lymphoma * Intravascular large B-cell lymphoma * B-cell lymphoma, unclassifiable, with features intermediate between DLBCL and classical Hodgkin lymphoma 2. Patients who, at the discretion of the investigator, need immediate cytoreductive chemotherapy such as patients with evidence of spontaneous tumor lysis or impending organ compromise are not eligible. 3. Current or prior anti-cancer treatment for DLBCL prior to enrollment. Short course of corticosteroids (\<7 days) for acute issues prior to study enrollment are permitted. 4. Major surgical procedure within 30 days of first dose of study drug. 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 5. Requires treatment with moderate or strong CYP3A inhibitors or inducers 6. Known lymphomatous involvement of the CNS 7. Pregnant individuals, or individuals who intend to become pregnant during the study are excluded from this study because of potential teratogenic effects associated with acalabrutinib, R-CHOP, and/or DA-EPOCH-R 8. The potential for all study treatments to be excreted in the milk of nursing mothers is unknown. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with acalabrutinib, nursing must be discontinued. 9. Uncontrolled intercurrent illness including, but not limited to the following that may limit interpretation of results or that could increase risk to the patient at the discretion of the investigator: -Other malignancy that requires ongoing systemic hormonal therapy, chemotherapy, or immunotherapy. Uncontrolled active systemic infection * Any condition that requires anticoagulation with warfarin or equivalent vitamin K antagonist * Active bleeding, history of bleeding diathesis (e.g., hemophilia or von Willebrand disease) * Suspected or confirmed Progressive Multifocal Leukoencephalopathy (PML) * Active hepatitis C infection. NOTE: Subjects who are hepatitis C antibody positive will need to have a negative HCV PCR result before enrollment. Those with a positive PCR for hepatitis C are excluded. * Active hepatitis B infection. NOTE: Patients who are hepatitis B surface antigen (HbsAg) positive will be excluded from enrollment. Patients who are hepatitis B core antibody (HbcAb) positive will need to have a negative HBV PCR result before enrollment. Those with a positive PCR for hepatitis B are excluded. Those who are hepatitis B core antibody (HbcAb) positive with a negative PCR for hepatitis B will be treated with antivirals designed to prevent hepatitis B reactivation (e.g., entecavir) throughout therapy and for 12 months after therapy and have monitoring for hepatitis B reactivation with PCR. * History of hemorrhagic stroke or intracranial hemorrhage in preceding 6 months * Clinically significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 6 months of screening, or any Class 3 (moderate) or Class 4 (severe) cardiac disease as defined by the New York Heart Association Functional Classification. Subjects with controlled atrial fibrillation/flutter during screening are eligible. * Uncontrolled autoimmune hemolytic anemia * Inability to swallow oral medications, or disease involve that significantly limits absorption of oral medication * Known mental or physical illness that would interfere with cooperation with the requirements of the trial or confound the results or interpretation of the results of the trial and, in the opinion of the treating investigator, would make the patient inappropriate for entry into the study. 10. Concurrent participation in another therapeutic clinical trial.