GLORY: Glofit-GemOx With Liso-Cel For Lymphoma

Inclusion Criteria: * Histologically confirmed large B-cell NHL including diffuse large B-cell lymphoma (DLBCL), either de novo or transformed from any indolent B-cell lymphoma, DLBCL NOS, primary mediastinal \[thymic\] large B-cell lymphoma (PMBCL), high grade B-cell lymphoma NOS, or high grade B-cell lymphoma with MYC and BCL2 and/or BCL6 rearrangements \[double/triple-hit lymphoma (DHL/THL)\]; and grade 3B follicular lymphoma. * Relapsed or refractory to 1 prior line of systemic lymphoma therapy if relapse/refractory within 12 months of initial treatment. Previous therapy must have included a CD20-targeted agent and an anthracycline or alkylating agent. Patients may have received steroids and/or polatuzumab-rituximab (without bendamustine), and/or radiation therapy for disease control and/or palliation "holding therapy" between frontline therapy and protocol registration and this will not be considered an additional line of systemic therapy. OR Relapsed or refractory to 1 prior line of systemic lymphoma therapy at any time after initial treatment if patient is ineligible for a stem cell transplant. Previous therapy must have included a CD20-targeted agent and an anthracycline or alkylating agent. Patients may have received steroids and/or polatuzumab-rituximab (without bendamustine), and/or radiation therapy for disease control and/or palliation "holding therapy" between frontline therapy and protocol registration and this will not be considered an additional line of systemic therapy. * Intent and eligibility to proceed to therapy with lisocabtagene maraleucel * Adult patients ≥ 18 years * PET-positive measurable disease per Lugano criteria * ECOG performance status 0-2 * Estimated creatinine clearance of ≥30 mL/min, calculated using the Cockcroft and Gault equation (if male: \[140 - Age\] x Mass \[kg\] / \[72 x creatinine g/dL\]; multiply by 0.85 if female) * Serum Aspartate Aminotransferase (AST) and Alanine Aminotransferase (ALT) ≤ 3 times the ULN * Total Bilirubin ≤1.5 x ULN, unless directly attributable to Gilbert-Meulengracht syndrome and ≤3.0 mg/dL * Absolute neutrophil count (ANC) ≥ 1000/mm3 (G-CSF support allowed if ≥ 24 hours prior to screening lab draw) * Hemoglobin ≥8g/dL * Platelets ≥ 50,000/mm3 without transfusion within 7 days * Patients with primary CNS lymphoma are not eligible. Patients with secondary CNS involvement by lymphoma are eligible if they otherwise meet all eligibility criteria. * The effects of glofitamab, gemcitabine, and oxaliplatin on the developing human fetus are unknown. For this reason and because immunotherapy/chemotherapy agents are known to be teratogenic, women of child-bearing potential and men must agree to use adequate double-method (each partner) contraception (acceptable means of birth control: condoms (male), condoms (female), intrauterine devices, contraceptive implants, combined hormonal contraceptives (pills, patches, vaginal rings), progestin-only pills, depot medroxyprogesterone acetate (DMPA) injections; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men and women treated or enrolled on this protocol must also agree to use adequate contraception for the duration of study participation, and 12 months after completion of lisocabtagene maraleucel administration. * Willing and able to participate in all required evaluations and procedures in this study protocol. * Ability to understand the purpose and risks of the study and provide signed and dated informed consent and authorization to use protected health information. * Ability to understand and agree to forgo donation of blood, organs, sperm, semen, or egg cells after treatment with liso-cel for 12 months. Exclusion Criteria: * History of prior malignancy that could affect compliance with the protocol or interpretation of results, except for the following: Non-melanoma skin cancers, in situ malignancies, prostate cancer followed with watchful waiting, indolent lymphoma, any previously treated malignancy felt at low risk for recurrence. * Evidence of disease (such as severe or uncontrolled systemic diseases) that, in the investigator's opinion, make it undesirable for the patient to participate in the study or that would jeopardize compliance with the protocol * Treatment with prior CAR T-cell therapy. * Treatment with prior CD20:CD3 bispecific antibody therapy. * History of or ongoing confirmed progressive multifocal leukoencephalopathy (PML) * Received any investigational drug within 30 days or 5 half-lives (whichever is shorter) before first dose of study drug. * Received a live virus vaccination within 28 days of first dose of study drug. * Concurrent participation in another therapeutic clinical trial. * Current life-threatening illness, medical condition, or organ system dysfunction which, in the Investigator's opinion, could compromise the subject's safety or put the study at risk * Previous treatment with gene therapy product or adoptive T cell therapy * Allogeneic stem cell transplant within 90 days of leukapheresis * Active acute or chronic GVHD requiring immunosuppressive therapy within 6 weeks prior to enrollment * Grade 2 or higher peripheral neuropathy * HIV infection with positive viral titer by PCR. HIV with negative viral titer by PCR is not an exclusion as long as CD4 count is ≥200 and patient is taking combination antiretroviral therapy. * Serologic status reflecting active hepatitis B or C infection 1. Subjects who are hepatitis B core antibody (HBcAb) positive and who are hepatitis B surface antigen (HBsAg) negative will need to have a negative PCR result before enrollment and must be willing to undergo DNA PCR testing during the study and take anti-HBV therapy with entecavir or equivalent. Those who are HBsAg-positive or hepatitis B PCR positive will be exclud