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 (FVC) \>= 50% of predicted * PART 1: Cardiac: Adequate cardiac function, defined as left ventricular ejection fraction (LVEF) of \>= 50%. Patients 60 years or older must have an LVEF at rest \>= 40%, as measured by echocardiogram or radionuclide ventriculogram scan (MUGA) * PART 1: Hematologic: Prothrombin time (PT)/international normalized ratio (INR) \< 1.5 x ULN and partial thromboplastin time PTT) (activated partial thromboplastin time \[aPTT\]) \< 1.5 x ULN, absolute neutrophil count (ANC) \>= 1000/mL, platelet \>= 75,000/uL * PART 1: Women of childbearing potential (WOCBP), defined as those who have not been surgically sterilized or who have not been free of menses for at least 1 year, must have a negative serum pregnancy test within 7 days of and prior to initiating loncastuximab tesirine in combination with BEAM conditioning * Fertile male and WOCBP subjects must be willing to use highly effective contraceptive methods before, during, and for at least 6 months after ASCT or 9 months after the last administration of loncastuximab tesirine for women, 6 months after the last administration of loncastuximab tesirine for men, whichever is longer * PART 1: Ability to provide informed consent * PART 2: Eligible disease status. Following ASCT (within day +30 to +90), subjects must have achieved radiographic partial response (PR) or complete response (CR) via PET/CT and/or diagnostic CT * PART 2: Targeted radiation therapy following ASCT is allowed but must be completed \>= 2 weeks prior to starting maintenance therapy * PART 2: Performance status ECOG 0-2 and/or Karnofsky \>= 60 * PART 2: CrCl \> 40 mL/min by Cockcroft-Gault formula or serum creatinine =\< 2.0 mg/dL * PART 2: Total bilirubin =\< 1.5 x the upper limit of normal (ULN) unless isolated hyperbilirubinemia attributed to Gilbert's syndrome; AST and ALT =\< 3 x ULN * PART 2: PT/INR \< 1.5 x ULN and PTT (aPTT) \< 1.5 x ULN, ANC \>= 1000/mL, platelet \>= 75,000/mL * PART 2: Pregnancy and the need for contraception. Negative serum pregnancy test within 7 days of initiating loncastuximab tesirine as maintenance therapy for women of childbearing potential (WOCBP), defined as those who have not been surgically sterilized or who have not been free of menses for at least 1 year * Fertile male and WOCBP patients must be willing to use highly effective contraceptive methods before, during, and for at least 6 months after ASCT or 16 weeks after the last administration of loncastuximab tesirine, whichever is longer Exclusion Criteria: * PART 1: Receiving other investigational agents * PART 1: History of central nervous system (CNS) involvement by lymphoma * PART 1: If a history of receiving a CD19 targeting agent (e.g., CD19 directed CAR T-cell Kymriah, Yescarta, Breyanzi, CD19 antibody Monjuvi), must have pathologic evidence for CD19 expression after receiving CD19 targeting agent * PART 1: History of immunogenicity or hypersensitivity to a CD19 antibody * PART 1: Uncontrolled bacterial, viral or fungal infection (currently taking medication and with progression or no clinical improvement); symptomatic congestive heart failure unresponsive to treatment, unstable angina pectoris, symptomatic cardiac arrhythmia not including premature ventricular contractions (PVC); or psychiatric illness/social situations that would limit compliance with study requirements * PART 1: Active autoimmune disease (e.g., rheumatoid arthritis, systemic progressive sclerosis \[scleroderma\], systemic lupus erythematosus, Sjogren's syndrome, autoimmune vasculitis \[e.g., granulomatosis with polyangiitis\]); motor neuropathy considered of autoimmune origin (e.g., Guillain-Barre syndrome and myasthenia gravis); other central nervous system (CNS) autoimmune disease (e.g., poliomyelitis, multiple sclerosis) * PART 1: Clinically significant third space fluid accumulation (i.e., ascites requiring drainage or pleural effusion that is either requiring drainage or associated with shortness of breath) * PART 1: Known seropositivity for human immunodeficiency virus (HIV), known history of hepatitis B or hepatitis C * PART 1: Active second primary malignancy other than non-melanoma skin cancers, non-metastatic prostate cancer, in situ cervical cancer, ductal or lobular carcinoma in situ of the breast, or other malignancy that the investigator(s) agreed and had documented that it was not exclusionary * PART 1: Any other significant medical illness, abnormality, or condition that could, in the investigator(s)' judgment, make the patient inappropriate for study participation or could put the patient at risk * PART 1: Evidence of myelodysplasia or cytogenetic abnormality indicative of myelodysplasia on bone marrow biopsy prior to initiation of therapy