Loncastuximab Tesirine for the Treatment of Relapsed or Refractory B-Cell Malignancies

Inclusion Criteria: * Male or female patient aged 18 years or older * Disease-specific criteria: * Group 1: CD19+ relapsed/refractory post-transplant lymphoproliferative disorder (PTLD), * Group 2: Relapsed/refractory. CD19+ B-cell non-Hodgkin lymphoma (B-NHL) excluding Waldenstrom's macroglobulinemia and marginal zone lymphoma, (at least 1 prior therapy, and no alternative with a more favorable benefit/risk ratio in the judgment of the treating investigator. * Group 3: CD19+ diffuse large B-cell lymphoma (DLBCL), follicular lymphoma (FL), or mantle cell lymphoma (MCL) relapsing after chimeric antigen receptor (CAR) T-cell therapy or allogeneic transplant (at least 30 days from CAR T/transplant) * Group 4: Relapsed/refractory, CD19-negative B-NHL by both immunohistochemistry and flow cytometry (minimal to absent expression). Patients (Pts) must have had at least 1 prior therapy, and no alternative with a more favorable benefit/risk ratio in the judgment of the treating investigator * Have measurable nodal or extranodal disease, including at least 1 disease site measuring 1.5 cm in longest dimension; or splenomegaly; or histologic marrow involvement for marrow-only presentations * Have a performance status of 0-2 on the Eastern Cooperative Oncology Group (ECOG) performance scale (PS) * Absolute neutrophil count (ANC) \>= 1.0 x 10\^3/uL (off growth factors at least 72 hours), unless due to marrow involvement by lymphoma in which case ANC must be \>= 0.5 x 10\^3/uL * Platelet count \>= 75 x 10\^3/uL without transfusion in the prior 7 days, unless due to disease including splenomegaly in which case platelet count must be \>= 50 x 10\^3/uL * Alanine aminotransferase (ALT), aspartate aminotransferase (AST), and gamma glutamyl transferase (GGT) =\< 3 x the upper limit of normal (ULN) * Total bilirubin =\< 1.5 x ULN (patients with known Gilbert's syndrome may have a total bilirubin up to =\< 3 x ULN) * Blood creatinine =\< 2.0 x ULN or calculated creatinine clearance \>= 50 mL/min by the Cockcroft and Gault equation * Negative beta-human chorionic gonadotropin (beta-HCG) pregnancy test within 7 days prior to start of study drug (cycle 1 day 1 \[C1D1\]) for women of childbearing potential * Women of childbearing potential must agree to use a highly effective method of contraception from the time of giving informed consent until at least 10 months after the last dose of loncastuximab tesirine * Men with female partners who are of childbearing potential must agree that they will use a condom from the time of giving informed consent until at least 7 months after the patient receives his last dose of loncastuximab tesirine Exclusion Criteria: * Previous treatment with loncastuximab tesirine * Known history of hypersensitivity to loncastuximab tesirine * 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 * Uncontrolled graft-versus-host disease * Has known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive or hepatitis B virus \[HBV\] deoxyribonucleic acid \[DNA\] detectable) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected) * Is pregnant, breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 9 months after the last dose of trial treatment * 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) * Lymphoma with active central nervous system (CNS) involvement at the time of screening, including active leptomeningeal disease. A history of treated CNS disease permitted * Significant medical comorbidities, including but not limited to unstable angina, congestive heart failure (New York Heart Association class III or greater), uncontrolled atrial or ventricular cardiac arrhythmia, that would, in the Investigator's judgment, make the patient inappropriate for study participation or put the patient at risk * Major surgery, radiotherapy, chemotherapy or other anti-neoplastic therapy within 14 days prior to start of study drug (C1D1) * Use of any other experimental medication within 14 days prior to start of study drug (C1D1) * Planned live vaccine administration after starting study drug (C1D1) * Any other significant medical illness, abnormality, or condition that would, in the investigator's judgment, make the patient inappropriate for study participation or put the patient at risk * Is currently participating in a study and receiving an investigational agent or is using an investigational device within 4 weeks of the first dose of treatment