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 A:

* Confirmed clinicopathological diagnosis of Waldenstrom macroglobulinemia (WM) in accordance with the consensus panel of the Second International Workshop on WM.
* Relapsed or refractory disease after 2 or more lines of therapy.

* Prior therapy must have included a Bruton's tyrosine kinase (BTK) inhibitor. Also, chemotherapy and/or a proteasome inhibitor must have been attempted, with either subsequent documented disease progression or no response (stable disease).
* Requiring treatment as defined in the recommendations from the Second International Workshop on WM.
* Measurable disease, defined as presence of serum immunoglobulin (Ig)M with a minimum IgM level of \> 2 times the upper limit of normal of each institution is required.
* The inclusion criteria concerning washout periods prior to leukapheresis in the master protocol must be met, with the exception that ibrutinib may be continued through leukapheresis and up to 5 half-lives (30 hours) prior to the start of lymphodepletion.

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.

Substudy D:

* Individuals must have histologically confirmed hairy cell leukemia (HCL) with a need for therapy based on at least one of the following criteria:

* neutrophils \< 1.0 x 10\^9/L
* platelets \< 100 x 10\^9/L
* hemoglobin \< 11 g/dL
* symptomatic splenomegaly
* symptomatic lymphadenopathy
* Individuals must have received:

* At least 2 prior therapies, including at least a purine nucleoside analog (PNA) and moxetumomab pasudotox if eligible and available.

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.
* History or presence of detectable cerebrospinal fluid malignant cells or brain metastases, with the exception of prior central nervous system (CNS) disease in WM.
* History of autoimmune disease (eg, Crohn's disease, rheumatoid arthritis, systemic lupus).

Substudy A:

* History of allogeneic stem cell transplantation. A prior autologous stem cell transplantation is allowed, but at least 6 months should have elapsed.
* Plasmapheresis for symptomatic hyperviscosity or serum IgM \> 5,000 mg/dL \< 35 days prior to the screening IgM assessment.
* Exclusion of IgM monoclonal gammopathy of undetermined significance or IgM multiple myeloma.
* Presence of CNS involvement (Bing-Neel syndrome). Individuals with a prior history of Bing-Neel syndrome are eligible if they show a negative cerebrospinal fluid (CSF) and no involvement by imaging.

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.

Substudy D:

* Prior history of allogeneic stem cell transplant.

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