Study Evaluating the Efficacy of KITE-753 Versus Axicabtagene Ciloleucel in Participants With Relapsed or Refractory Large B-Cell Lymphoma After First-Line Therapy

Key Inclusion Criteria: * Individuals with any of the following large B-cell lymphomas, as determined by the investigator, are eligible for the study as defined below: * World Health Organization (WHO): * Individuals with chemorefractory disease to first-line therapy (primary refractory disease) that satisfies any of the following criteria: * Progressive disease (PD) and/or Deauville score of 5 (irrespective of the response designation) as the best response during the first-line treatment or as the end of treatment response following first-line therapy. * Stable disease (SD) after at least 4 cycles of first-line therapy (eg, 4 cycles of rituximab plus cyclophosphamide, doxorubicin, vincristine, and prednisone (R-CHOP)). * PR as best response after at least 6 cycles of first-line therapy (eg, 6 cycles of R-CHOP). * Note: A biopsy is recommended to confirm residual disease. * Individuals with relapsed disease defined as complete remission to first-line therapy followed by biopsy-proven disease relapsed ≤ 12 months of completion of first-line therapy. * Note: If the relapse is confirmed by imaging per International Working Group (IWG) Lugano Response Criteria for Malignant Lymphoma within 12 months, the confirmatory biopsy must be performed within 90 days of the 12-month cutoff. * Prior therapy must have included an anti-CD20 antibody (including CD20-targeting T-cell engager antibodies) and an anthracycline-containing chemotherapy regimen. * For individuals with transformed indolent NHL, therapies given for non-transformed disease do not count as a line of therapy for the transformed disease. * Individuals who have had no additional systemic therapy or holding therapy (except for steroids and/or local radiation) following first-line therapy and prior to leukapheresis are eligible. * At least 1 measurable lesion according to the IWG Lugano Response Criteria. Lesions that have been previously irradiated will be considered measurable only if progression has been documented following completion of radiation therapy. A measurable lesion is defined as \>1.5 cm longest transverse diameter (LDi) for lymph node and \> 1.0 cm LDi for extranodal lesion. Splenomegaly or hepatomegaly alone in the absence of a measurable lesion is not considered to be measurable disease. * The following washout period must be satisfied: * At least 2 weeks or 5 half-lives, whichever is shorter, must have elapsed since any prior systemic therapy at the time the individual is randomized. * Toxicities due to immediate prior therapy must have recovered to Grade 1 or lower (except for clinically nonsignificant toxicities such as alopecia, unless otherwise specified in the protocol) * Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 2. * Adequate bone marrow function as evidenced by: * Absolute neutrophil count ≥ 1,000/μL or ≥ 500/μL if documented bone marrow involvement of lymphoma. Bone marrow involvement by lymphoma is demonstrated by positron emission tomography (PET) scan or bone marrow aspiration or bone marrow biopsy. * Platelet count ≥ 75,000/μL (unless secondary to bone marrow or spleen involvement by lymphoma, in which platelet count ≥ 50,000 μL is permitted). Bone marrow involvement by lymphoma is demonstrated by PET scan or bone marrow aspiration or bone marrow biopsy. Spleen involvement by lymphoma is demonstrated by PET-diagnostic computed tomography (CT) involvement, splenomegaly, or biopsy. * Adequate renal, hepatic, cardiac, and pulmonary function as evidenced by: * Creatine clearance (as estimated by Cockcroft-Gault formula) ≥ 30 mL/minute. Note: 24-hour urine estimate is also acceptable. * Serum alanine aminotransferase/aspartate aminotransferase ≤ 3.0 times the upper limits of normal, except in individuals with documented liver involvement by lymphoma via PET-diagnostic CT scan or biopsy * Total bilirubin ≤ 1.5 mg/dL, except in individuals with Gilbert's Syndrome or documented liver or pancreatic involvement where ≤ 3.0 times the upper limit of normal is permitted * Cardiac ejection fraction ≥ 40% and no pericardial effusion Grade 3 or higher (per Common Terminology Criteria for Adverse Events (CTCAE) version (v)5.0) as determined by an echocardiogram (ECHO) or multiple-gated acquisition scan (MUGA) (if ECHO not available at the site). Note: If there is any concern for pericardial effusion, an ECHO must be performed since MUGA alone is not an adequate modality to assess for pericardial effusion. * No evidence of Grade 2 (per CTCAE v5.0) or greater pleural effusion or ascites (individuals with Grade 1 ascites or pleural effusion are eligible) * Baseline oxygen saturation \> 92% on room air * Females of childbearing potential must have a medically supervised negative serum or urine pregnancy test (females who have undergone surgical sterilization or have been postmenopausal for at least 2 years before randomization are not considered to be of childbearing potential. Key Exclusion Criteria: * Prior CAR T-cell therapy or other cell-based therapy. * History of malignancy other than nonmelanoma skin cancer or carcinoma in situ (eg, cervix, bladder, or breast) unless disease-free and without anti-cancer therapy (with the exception of hormonal therapy in the case of breast cancer) for at least 3 years. Individuals with asymptomatic localized low-grade prostate cancer for which a watch-and-wait approach is standard of care are eligible. * Individuals with the following LBCL fifth edition of WHO criteria subtypes: Richter's transformation of chronic leukemic lymphoma, small lymphocytic lymphoma, Burkitt lymphoma, lymphoplasmacytic lymphoma, T-cell/histiocyte-rich LBCL, mediastinal gray zone lymphoma, plasmablastic lymphoma, intravascular LBCL, primary central nervous system (CNS) lymphoma, primary vitreoretinal LBCL, fibrin-associated LBCL, fluid overload-associated LBCL lymphomatoid granulomatosis, high-grade B-cell lymphoma (HGBCL) with 11q aberrations, anaplastic lymphoma kinase-positive LBCL, LBCL with Interferon Regulatory Factor 4 (IRF4) rearrangement, and transformed from Hodgkin's lymphoma (HL). Note: Individuals with primary testicular LBCL are eligible. * History of a severe, immediate hypersensitivity reaction attributed to aminoglycosides * Presence or suspicion of fungal, bacterial, viral, or other infection that is uncontrolled or requires intravenous (IV) antimicrobials for management. Note: Simple urinary tract infections and uncomplicated bacterial or viral upper respiratory tract infections are permitted if the individual is responding to active treatment and satisfies the criteria of being afebrile for 48 hours (ie, temperature \< 38°C). * Known history of hepatitis B virus (HBV) (hepatitis B surface (HBs) antigen (HBsAg) positive) infection, or hepatitis C (anti-hepatitis C virus (HCV)) positive) infection. History of a hepatitis B or C infection is permitted if the viral load is undetectable per quantitative polymerase chain reaction (qPCR) or nucleic acid testing. Note: Individuals who are seropositive for HBV (ie, HBs and/or hepatitis B core antibody positive) are eligible if they are HBsAg-negative and negative for viral DNA. Individuals who are seropositive because of HBV vaccination are eligible (ie, HBs antibody positive, hepatitis core antibody-negative, and HBsAg-negative). Individuals on prophylactic and suppressive antiviral medications against HBV and/or HCV administered per institutional or clinical practice guidelines are eligible. * HIV-positive, unless taking appropriate anti-HIV medications, with an undetectable viral load by qPCR and a CD4 count ≥ 200 cells/μL. Note: HIV-positive individuals in Australia are not permitted regardless of active antiretroviral therapy or undetectable blood viral load. * History or presence of the following CNS disorders: hemorrhage, dementia (per CTCAE v5.0 Grade 2 or higher memory impairment), cerebellar disease, any autoimmune disease with CNS involvement, posterior reversible encephalopathy syndrome, or cerebral edema with confirmed structural defects by appropriate imaging. * History of stroke or transient ischemic attack within 6 months before enrollment. Individuals with seizure disorders requiring active anticonvulsive medication. * Individuals with cardiac atrial or cardiac ventricular lymphoma involvement. * Individuals with secondary CNS lymphoma. * Individuals with full thickness lymphoma involvement of gastric or intestinal lining. Individuals with concern for gastric or intestinal perforation or known contained perforation. * History of myocardial infarction, cardiac angioplasty or stenting, unstable angina, active unstable/uncontrolled arrhythmia, New York Heart Association Class II or greater congestive heart failure, or other clinically significant cardiac disease within the 6 months before enrollment. * Requirement for urgent therapy within 4 weeks before enrollment due to ongoing or impending oncologic emergency (eg, tumor mass effect) * Presence of primary immunodeficiency. * History of any medical condition including but not limited to autoimmune disease (eg, Crohn's, rheumatoid arthritis, or systemic lupus) resulting in end organ injury or requiring systemic immunosuppression and/or systemic disease-modifying agents within the last 90 days. Note: At least 90 days or 5 half-lives, whichever is shorter, must have elapsed after any prior immunosuppressive or immunomodulating therapy that impacts T-cell function and before leukapheresis. * History of concomitant genetic syndrome associated with bone marrow failure such as Fanconi anemia, Kostmann syndrome, or Shwachman-Diamond syndrome. * Any medical condition or residual toxicities from prior therapies per investigator assessment likely to interfere with the assessments of safety or efficacy of the study treatment. * History of a severe immediate hypersensitivity reaction or contraindication to any of the agents used in the study (including fludarabine and cyclophosphamide). * Live vaccine ≤ 6 weeks before randomization, during the treatment period, and until immune recovery following the study treatments (refer to Section 12.10 for additional country-specific requirements, as applicable). * Females of childbearing potential who are pregnant or breastfeeding because of the potentially dangerous effects of the preparative chemotherapy on the fetus or infant. Females who have undergone surgical sterilization or have been postmenopausal for at least 2 years are not considered to be of childbearing potential. * Individuals of either sex who are not willing to practice highly effective birth control from the time of informed consent through 12 months after the completion of KITE-753 or axi-cel infusion. * In the investigator's judgment, the individual is unlikely to complete all study-specific visits or procedures, including follow-up visits, or comply with the study requirements for participation. Note: Other protocol defined Inclusion/Exclusion criteria may apply.