Loncastuximab Tesirine in Combination With Chemotherapy Prior to Stem Cell Transplant for the Treatment of Recurrent or Refractory Diffuse Large B-Cell Lymphoma

Inclusion Criteria: * PART 1: Subjects must have a histologically confirmed diagnosis of diffuse large B-cell lymphoma including diffuse large B-cell lymphoma (DLBCL) not otherwise specified, primary mediastinal large B-cell lymphoma, high grade B-cell lymphoma (with MYC and BCL-2 and/or BCL-6 gene rearrangement), and DLBCL arising from follicular lymphoma * PART 1: Subjects must be eligible for high-dose therapy (BEAM conditioning chemotherapy) and autologous stem cell transplant, as determined by transplant center * PART 1: Subjects must have chemosensitive disease as defined radiographically (positron emission tomography \[PET\]/computed tomography \[CT\] and/or diagnostic CT) by at least a partial response (PR) to their last cycle of salvage therapy, within 60 days of enrollment * PART 1: Subjects must be \>= 18 years of age * PART 1: Eastern Cooperative Oncology Group (ECOG) score =\< 2 or Karnofsky score \>= 60% * PART 1: Creatinine clearance (CrCl) \> 40 mL/min by Cockcroft-Gault formula or serum creatinine =\< 2.0 mg/dL * PART 1: Total bilirubin =\< 1.5 x the upper limit of normal (ULN) unless isolated hyperbilirubinemia attributed to Gilbert's syndrome; aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3 x ULN * PART 1: Adequate pulmonary function, defined as lung carbon monoxide diffusing capability test (DLCO) (corrected or uncorrected for hemoglobin per institutional standards), forced expiratory volume in 1 (FEV1), forced vital capacity (FV…