Key Inclusion Criteria:

All Substudies:

* Presence of toxicities due to prior therapy must be stable and recovered to Grade 1 or lower.
* Eastern Cooperative Oncology Group (ECOG) performance status score of 0 or 1
* Adequate hematologic and end-organ function.
* Individuals of childbearing potential who engage in heterosexual intercourse must agree to use specified method(s) of contraception.

Substudy B:

* Confirmed diagnosis of chronic lymphocytic leukemia (CLL) based on International Workshop on Chronic Lymphocytic Leukemia (IWCLL) 2018 criteria with histologically confirmed Richter transformation (RT) to a diffuse large B-cell lymphoma (DLBCL) subtype.
* Relapsed or refractory disease after 1 line of therapy, defined as at least 1 of the following:

* Refractory disease, defined as progressive disease or stable disease as best response to first-line therapy.
* Relapsed disease, defined as complete remission to first-line therapy followed by biopsy-proven disease relapse.
* At least 1 measurable lesion based on the Lugano Classification. Lesions that have been previously irradiated will be considered measurable only if progression has been documented following completion of radiation therapy.

Substudy C:

* Histologically confirmed mature B-cell non-Hodgkin lymphoma (NHL) Burkitt lymphoma/leukemia.
* Relapsed or refractory disease after first-line chemoimmunotherapy, defined as 1 of the following:

* Refractory disease, defined as progressive disease or stable disease as best response to first-line therapy; individuals who are intolerant to first-line therapy are excluded.
* Relapsed disease, defined as complete remission to first-line therapy followed by biopsy-proven disease relapse.
* At least 1 measurable lesion based on the Lugano Classification. Lesions that have been previously irradiated will be considered measurable only if progression has been documented following completion of radiation therapy.

Key Exclusion Criteria:

All Substudies:

* Prior CAR therapy or treatment with any anti-CD19 therapy.
* HIV-positive patients, unless taking appropriate anti-HIV medications, having an undetectable viral load by quantitative polymerase chain reaction (qPCR) and a CD4 count \> 200 cells/uL.
* Presence of detectable cerebrospinal fluid malignant cells or brain metastases.
* History of autoimmune disease (eg, Crohn's disease, rheumatoid arthritis, systemic lupus).

Substudy B:

* Diagnosis of RT not of DLBCL subtype (including, but not limited to, Hodgkin lymphoma (HL) and prolymphocytic leukemia).
* Prior allogeneic or autologous stem cell transplant \< 3 months prior to screening and/or \< 4 months prior to planned infusion of brexucabtagene autoleucel.
* Presence of active graft-versus-host disease following prior stem cell transplant.

Substudy C:

* Burkitt-like lymphoma with 11q aberration, high-grade B-cell lymphoma with MYC and BCL2 and/or BCL6 rearrangement, or high-grade B-cell lymphoma not otherwise specified.
* Prior allogeneic stem cell transplant \< 3 months prior to screening and/or \< 4 months prior to planned infusion of brexucabtagene autoleucel.
* Presence of active graft-versus-host disease following prior allogeneic stem cell transplant.
* Presence of CNS involvement. Individuals with a prior history of CNS involvement are eligible if they show a negative CSF and no involvement by imaging.

Substudies A and D have been early terminated by the sponsor.

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