Key Inclusion Criteria:

* 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:

* 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 Richter's transformation of chronic leukemic lymphoma, small lymphocytic lymphoma, or lymphoplasmacytic lymphoma.
* 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.
* Individuals with detectable cerebrospinal fluid (CSF) malignant cells or brain metastases or a history of central nervous system (CNS) lymphoma, primary CNS lymphoma, or spinal epidural involvement.
* 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 2 years.
* History of non-line associated, clinically significant deep-vein thrombosis or pulmonary embolism requiring therapeutic anticoagulation within the 6 months before enrollment.
* 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.