Loncastuximab Tesirine in Combination With DA-EPOCH-R in Patients With Previously Untreated Aggressive B-cell Lymphoid Malignancies

Inclusion Criteria: 1. Age ≥ 18 years. 2. Adult patients with B-cell lymphoma, specifically one of the following: high-grade B-cell lymphoma with MYC and B-cell lymphoma 2 (BCL2) and/or B cell lymphoma 6 (BCL6) rearrangements; high-grade B-cell lymphoma, not otherwise specified, primary mediastinal diffuse large B-cell lymphoma; Burkitt lymphoma; diffuse large B-cell lymphoma with MYC rearrangement; or Cluster of Differentiation 19 (CD19) -positive plasmablastic lymphoma. 3. Patients must not have received prior multiagent chemotherapy for their lymphoma. Limited palliative radiation is allowed. Corticosteroid therapy in symptomatic patients will be permitted and does not require a washout period. Prephase treatment with cyclophosphamide and corticosteroids or vincristine and corticosteroids is allowed in symptomatic patients. 4. Eastern Cooperative Oncology Group (ECOG) Performance Status criteria of 0-3. 5. Adequate hematological function, defined as absolute neutrophil count (ANC) ≥1 × 103/μL and platelet count ≥50 x 10\^3/μL. \- These requirements do not apply to patients with bone marrow involvement of lymphoma. 6. Adequate hepatic function: aspartate aminotransferase (AST) / alanine aminotransferase (ALT) / gamma-glutamyl transferase (GGT) ≤ 3 x institutional upper limit of normal (ULN) and bilirubin \< 1.5 x ULN, unless due to hepatic involvement with lymphoma or Gilbert's syndrome. \- Exceptions can be granted from principal investigator for primarily indirect bilirubinemia if due to recent transfusion and/or hemolysis. 7. Creatinine clearance ≥ 30 ml/min calculated using the Cockroft-Gault formula. 8. Left ventricular ejection fraction (LVEF) of ≥50%, assessed by echocardiography or cardiac multi-gated acquisition (MUGA) scan. 9. Patients with marrow-only disease will be eligible. 10. Patients rendered no evidence of disease via surgery will be eligible. 11. Central nervous system (CNS) involvement is not considered contraindication for patients with Burkitt lymphoma. 12. Known HIV-positive patients compliant with antiretroviral therapy and with undetectable viral loads will be permitted. 13. Pregnancy It is not known what effects this treatment has on human pregnancy or development of the embryo or fetus. Therefore, female patients participating in this study should avoid becoming pregnant, and male patients should avoid impregnating a female partner. Non-sterilized female patients of reproductive age and male patients should use effective methods of contraception through defined periods during and after study treatment as specified below. * Female patients of childbearing potential must use a highly effective method of contraception during the entire study treatment period and through nine months after the last dose of loncastuximab tesirine. * Male patients, even if surgically sterilized (i.e., status postvasectomy), with female partners who are of childbearing potential should use a condom when sexually active during the entire study treatment period and through six months after the last dose of loncastuximab tesirine. 14. Ability to understand a written informed consent document, and the willingness to sign it. Exclusion Criteria: 1. Presence of clinically significant pericardial or pleural effusions, or third space fluid accumulations (i.e., ascites requiring drainage or pleural effusion that is either requiring drainage or associated with shortness of breath). 2. Known history of hypersensitivity to CD19 antibody, components of study medication, or DA-EPOCH-R. 3. Serologic evidence of chronic hepatitis B virus (HBV) infection and unable or unwilling to receive standard prophylactic antiviral therapy. These subjects MUST HAVE undetectable HBV viral load to be considered for this protocol. 4. Serologic evidence of hepatitis C virus (HCV) infection without completion of curative treatment or with detectable HCV viral load. 5. Breastfeeding or pregnant. 6. Active systemic bacterial, viral, fungal, or other infection requiring systemic treatment at time of screening. 7. Congenital long QT syndrome or a corrected QT measure (QTc) interval of \>480 ms at screening (unless secondary to pacemaker or bundle branch block). 8. Patients diagnosed with another malignancy within three years or with any evidence of residual prior malignant disease (except nonmelanoma skin cancer, non-metastatic prostate cancer, in situ cervical cancer, or ductal or lobular carcinoma in situ). Patients meeting this exclusion criteria may be enrolled after approval from study PI. 9. Significant medical comorbidities such as New York Heart Association class ≥III heart failure, unstable angina, uncontrolled arrhythmias, or severe chronic pulmonary disease. 10. Lymphoma with active CNS involvement at time of screening unless the patient has Burkitt lymphoma. 11. Patient with known intraparenchymal CNS involvement (including those with Burkitt lymphoma). 12. Patients with known Child Pugh Class C hepatic impairment.