Loncastuximab Tesirine and Rituximab as Bridging Therapy Before Standard-of-care CAR-T Therapy in Patients With Large B-cell Lymphoma (CORAL)

Inclusion Criteria: * Subject aged ≥ 18 years. * Intended to receive commercial CD19-directed CAR-T cell therapy (axi-cel and liso-cel). * Need for bridging therapy as deemed clinically necessary by the treating physician. * Relapsed or refractory DLBCL, tFL or PMBCL as defined by the 2016 World Health Organization classification (including patients with DLBCL transformed from indolent lymphoma), or high-grade B-cell lymphoma (HGBL), not otherwise specified, and HGBL 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. * 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 the tumor is not fluorodeoxyglucose (FDG)-avid on screening PET-CT. * ECOG Performance Status ≤ 2. * Time between prior anticancer therapy and first dose of lonca-R as below * Autologous hematopoietic cell transplantation - At least 30 days * Allogeneic hematopoietic cell transplantation - At least 60 days * Cytotoxic chemotherapy - At least 21 days * Non-cytotoxic chemotherapy (e.g., small molecule inhibitor) - At least 14 days * Adequate organ function as defined as: * Hematologic: * Absolute neutrophil count (ANC) ≥ 1000/mm3 * Platelet count ≥ 75,000/mm3 * Hemoglobin ≥ 8 g/dL * Hepatic: * Bilirubin ≤1.5 x upper limit of normal (ULN) or ≤3 x ULN with document liver involvement and/ or Gilbert's disease * Transaminases (AST or ALT) ≤ 3 x ULN or ≤ 5 x ULN with documented liver involvement * Renal: * Estimated creatinine clearance ≥ 60 mL/min by Cockcroft-Gault formula. * For female subjects: Negative pregnancy test or evidence of post-menopausal status. The post-menopausal status will be defined as having been amenorrheic for 12 months without an alternative medical cause. The following age-specific requirements apply: * Women \< 50 years of age: * Amenorrheic for ≥ 12 months following cessation of exogenous hormonal treatments; and * Luteinizing hormone and follicle-stimulating hormone levels in the post-menopausal range for the institution; or * Underwent surgical sterilization (bilateral oophorectomy or hysterectomy). * Women ≥ 50 years of age: * Amenorrheic for 12 months or more following cessation of all exogenous hormonal treatments; or * Had radiation-induced menopause with last menses \>1 year ago; or * Had chemotherapy-induced menopause with last menses \>1 year ago; or * Underwent surgical sterilization (bilateral oophorectomy, bilateral salpingectomy, or hysterectomy). * Female subjects of childbearing potential and male subjects with a sexual partner of childbearing potential must agree to use a highly effective method of contraception and the lactation requirements as described in Sections 5.41.1 and 5.4.2. * Subjects or their legal representatives must be able to read, understand, and provide informed consent to participate in the trial. * Willing and capable of giving signed informed consent which includes compliance with the requirements and restrictions listed in the informed consent form (ICF) and in the protocol Exclusion Criteria: * Previous treatment with any anti-CD19 therapy including lonca or prior CD19 CAR T-cell therapy * Subjects receiving investigational CAR-T products * Major surgery within 4 weeks prior to starting study therapy. * History of bleeding diathesis (e.g., von Willebrand's disease), hemophilia, or active bleeding. * Subjects with chronic liver disease with hepatic impairment Child-Pugh class C * Pregnant or lactating or intending to become pregnant during the study * Active graft-versus-host disease * Post-transplantation lymphoproliferative disorders * Active autoimmune disease which, in the opinion of the investigator, may negatively impact subject safety or interfere with study participation. * The diagnosis of another malignancy which, in the opinion of the investigator, is likely to negatively impact subject safety or interfere with study participation. * Subjects with known CNS involvement. * Significant medical diseases or conditions including those requiring substantial changes in concomitant medications, as assessed by the investigator, that would substantially increase the risk-to-benefit ratio of participating in the study. This includes, but is not limited to the following conditions: * Cardiovascular disorders: * Congestive heart failure New York Heart Association Class III or IV, unstable angina pectoris, serious cardiac arrhythmias. * Myocardial infarction (MI) within 6 months before the first dose. * QTc prolongation defined as a QTcF \> 480 ms. * Congenital long QT syndrome or a corrected QT measure (QTc) interval of \>480 ms at screening (unless secondary to pacemaker or bundle branch block). * Severe pulmonary disease * Uncontrolled diabetes mellitus * Severely immunocompromised state * Any other condition that would, in the Investigator's judgment, contraindicate the subject's participation in the clinical study due to safety concerns or compliance with clinical study procedures. * Active systemic bacterial, viral, fungal, or other infection requiring systemic treatment at time of screening * HIV infection. * Subjects with evidence of active hepatitis B infection, based on positive surface antigen or Hepatitis B DNA PCR are excluded. Subjects who are Hepatitis B core antibody positive must take prophylaxis with entecavir or equivalent and be willing to undergo monthly Hepatitis B DNA PCR testing. Subjects with active Hep C patients may be enrolled if other parameters precluding hepatic impairment are met and they are not undergoing active therapy for hepatitis C. * Known prior severe hypersensitivity to a CD19 antibody, lonca (including SG3249) or any of its excipients, or history of positive serum human ADA to a CD19 antibody. * Subjects taking prohibited medications as described in Section 6.8.1. A washout period of prohibited medications for a period of at least five half-lives or as clinically indicated should occur before the start of treatment.