The goal of this clinical study is to learn more about the safety and effectiveness of the study drugs, KITE-363 and KITE-753, in participants with relapsed and/or refractory B-cell lymphoma.

Eligible study participants who have received IP administration with either KITE-363 or KITE-753 will transition to a separate Long-term Follow-up study (Study KT-US-982-5968) to complete the remainder of the 15-year follow-up assessments.

Key Inclusion Criteria: for Phase 1a/b and Phase 2

• Relapsed and/or refractory B-cell lymphoma (R/R BCL).
• At least 1 measurable lesion.
• Adequate organ and bone marrow (BM) function.

Key Exclusion Criteria: for Phase 1a/b and Phase 2

- History of chimeric antigen receptor (CAR) therapy or other genetically modified T cell therapy.

• History of malignancy other than nonmelanoma skin cancer or carcinoma in situ (eg, cervix, bladder, or breast) unless disease free and without anticancer therapy (with the exception of hormonal therapy in the case of breast cancer) for at least 3 years.
• History of allogeneic stem cell transplant (allo-SCT).
• Auto-SCT within 6 weeks before the planned KITE-363 or KITE-753 infusion.
• Presence of fungal, bacterial, viral, or other infection that is uncontrolled or requires intravenous (IV) antimicrobials for management.
• Known history of human immunodeficiency virus (HIV) infection, 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.
• Individuals with suspicion and/or evidence of primary or secondary CNS lymphoma.
• History or presence of a CNS disorder.
• History of myocardial infarction, cardiac angioplasty or stenting, unstable angina, active arrhythmia, New York Heart Association Class II or greater congestive heart failure or other clinically significant cardiac disease within the 6 months before enrollment.
• Primary immunodeficiency.
• History of autoimmune disease resulting in or requiring systemic immunosuppression and/or systemic disease-modifying agents within the last 90 days.
• Individuals with full thickness lymphoma involvement of the gastric or intestinal lining and/or transmural gastrointestinal (GI) tract involvement, or with concern for gastric or intestinal perforation or known contained gastric or intestinal perforation.
• 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.

Note: Other protocol defined Inclusion/Exclusion criteria may apply.