Inclusion Criteria:

          -  Male or female participant aged 18 years or older

          -  Pathologic diagnosis of DLBCL, as defined by the 2016 World Health Organization
             classification (including participants with DLBCL transformed from indolent lymphoma),
             or high-grade B-cell lymphoma, with MYC and BCL2 and/or BCL6 rearrangements

          -  Relapsed (disease that has recurred following a response) or refractory (disease that
             failed to respond to prior therapy) disease following at least one multi-agent
             systemic treatment regimen

          -  Not considered by the investigator to be a candidate for stem cell transplantation
             based on performance status, advanced age, and/or significant medical comorbidities
             such as organ dysfunction

          -  Participants who have received previous CD19-directed therapy must have a biopsy which
             shows CD19 expression after completion of the CD19-directed therapy

          -  Measurable disease as defined by the 2014 Lugano Classification as assessed by
             positron-emission tomography (PET)- computed tomography (CT) or by CT or magnetic
             resonance imaging (MRI) if tumor is not fluorodeoxyglucose (FDG)-avid on screening
             PET-CT

          -  Availability of formalin-fixed paraffin-embedded (FFPE) tumor tissue block (or minimum
             10 freshly cut unstained slides if block is not available) Note: Any biopsy since
             initial diagnosis is acceptable, but if several samples are available, the most recent
             sample is preferred

          -  ECOG performance status 0-2

          -  Adequate organ function as defined by screening laboratory values within the following
             parameters:

               1. Absolute neutrophil count ≥1000/μL (off growth factors for at least 72 hours)

               2. Platelet count ≥75000/μL without transfusion within the past 2 weeks

               3. ALT, AST, and GGT ≤2.5 × the upper limit of normal (ULN)

               4. Total bilirubin ≤1.5 × ULN (participants with known Gilbert's syndrome may have a
                  total bilirubin up to ≤3 × ULN)

               5. Calculated creatinine clearance ≥30 mL/min by the Cockcroft and Gault equation

        Note: A laboratory assessment may be repeated a maximum of two times during the Screening
        period to confirm eligibility.

          -  Negative beta-human chorionic gonadotropin (β-hCG) pregnancy test within 7 days prior
             to start of study drug (Cycle 1 Day 1) for women of childbearing potential

          -  Women of childbearing potential (WOCBP) must agree to use a highly effective method of
             contraception from the time of giving informed consent until at least 9 months after
             the last dose of loncastuximab tesirine. Men with female partners who are of
             childbearing potential must agree that they will use a highly effective method of
             contraception from the time of giving informed consent until at least 6 months after
             the participant receives his last dose of loncastuximab tesirine.

        Exclusion Criteria:

          -  Previous treatment with loncastuximab tesirine

          -  Previous treatment with R-GemOx

          -  Known history of hypersensitivity to or positive serum human ADA to a CD19 antibody

          -  Pathologic diagnosis of Burkitt lymphoma

          -  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 Sponsor's medical monitor and Investigator agree
             and document should not be exclusionary

          -  Autologous transplant within 30 days prior to start of study drug (Cycle 1 Day 1)

          -  Allogeneic transplant within 60 days prior to start of study drug (Cycle 1 Day 1)

          -  Active graft-versus-host disease

          -  Post-transplantation lymphoproliferative disorders

          -  Active autoimmune disease, including motor neuropathy considered of autoimmune origin
             and other central nervous system (CNS) autoimmune disease

          -  Human immunodeficiency virus (HIV) seropositive with any of the following:

               1. CD4+ T-cell (CD4+) counts <350 cells/μL

               2. Acquired immunodeficiency syndrome-defining opportunistic infection within 12
                  months prior to screening

               3. Not on anti-retroviral therapy, or on anti-retroviral therapy for <4 weeks at the
                  time of screening

               4. HIV viral load ≥400 copies/mL

          -  Serologic evidence of chronic hepatitis B virus (HBV) infection and unable or
             unwilling to receive standard prophylactic antiviral therapy or with detectable HBV
             viral load

          -  Serologic evidence of hepatitis C virus (HCV) infection without completion of curative
             treatment or with detectable HCV viral load

          -  History of Stevens-Johnson syndrome or toxic epidermal necrolysis

          -  Lymphoma with active CNS involvement, including leptomeningeal disease

          -  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)

          -  Breastfeeding or pregnant

          -  Uncontrolled hypertension (blood pressure ≥160/100 mm Hg repeatedly), unstable angina,
             congestive heart failure (greater than New York Heart Association class II),
             electrocardiographic evidence of acute ischemia, coronary angioplasty or myocardial
             infarction within 6 months prior to screening, uncontrolled atrial or ventricular
             cardiac arrhythmia, poorly controlled diabetes, severe chronic pulmonary disease, or
             other serious medical condition which is likely to significantly impair the
             participant's ability to tolerate the study treatment

          -  Major surgery, radiotherapy, chemotherapy or other antineoplastic therapy within 14
             days prior to start of study drug (Cycle 1 Day 1), except shorter if approved by the
             Sponsor

          -  Use of any other experimental medication within 14 days or 5 half-lives prior to start
             of study drug (Cycle 1 Day 1)

          -  Received live vaccine within 4 weeks of Cycle 1 Day 1

          -  Failure to recover to ≤Grade 1 (Common Terminology Criteria for Adverse Events [CTCAE]
             version 5.0) from acute non-hematologic toxicity (except alopecia) due to previous
             therapy prior to screening

          -  Congenital long QT syndrome or a corrected QTcF interval of ≥480 ms at screening
             (unless secondary to pacemaker or bundle branch block)

          -  Any other significant medical illness, abnormality, or condition that would, in the
             Investigator's judgment, make the participant inappropriate for study participation or
             put the participant at risk

          -  Known history of hypersensitivity to oxaliplatin or any of its excipients