• Criteria for B-ALL:

• Participant has unequivocal r/r CD19+ B-ALL that has been confirmed by morphology, flow cytometry, or a validated minimal residual disease (MRD) assay.

• Participants with Philadelphia chromosome positive disease can be eligible if they are intolerant to tyrosine kinase inhibitor therapy or if they have r/r disease.

• Criteria for NHL:

• Participant has unequivocal aggressive CD19+ r/r B-cell NHL that is confirmed by archived tumor biopsy tissue from last relapse after CD19-directed therapy and corresponding pathology report. Alternatively, if at least 1 tumor involved site is accessible at time of Screening, the participant's diagnosis is confirmed by pretreatment biopsy (excisional when possible) or by flow cytometry of fine needle aspirate (FNA). If a participant never had a CR, a sample from the most recent biopsy is acceptable. NHL subtypes included but are not limited to:

• For Phase 1 Dose Escalation:

‣ Diffuse large B-cell lymphoma (DLBCL) including Richter's transformation

⁃ FL including Grade 3 or transformed FL

⁃ High-grade B-cell lymphoma

⁃ Primary mediastinal lymphoma

• For Phase 1b Dose Expansion:

‣ DLBCL not otherwise specified (NOS)

⁃ High grade B-Cell Lymphoma

⁃ DLBCL transformed from the following indolent lymphoma subtypes (Follicular lymphoma, Marginal Zone lymphoma and Waldenstrom's Macroglobulinemia)

• Participant has measurable or detectable (for example positron emission tomography-positive) disease according to the Lugano Classification.

• Participant must have received at least 2 lines of prior anti-cancer therapy for the disease under study, including at least 1 chemoimmunotherapy regimen (e.g., anti-CD20 monoclonal antibody plus chemotherapy), consistent with standard of care treatment guidance (e.g., National Comprehensive Cancer Network \[NCCN\]), unless no second line therapy of known benefit exists for a given subject. For Richter's transformation, only 1 prior line of therapy is required for the DLBCL component.

• Participant has received no more than 7 systemic lines of anti-cancer therapy for the disease under study.

• Participants previously treated with CD19-directed autologous CAR T therapies have received no more than 2 lines of therapy after administration of their previous CAR T product.

• Expansion cohort only: Participants must have received autologous CD19-directed CAR T therapy and demonstrated clinical response to the treatment at Day 28 or later, followed by relapse or progression.

• Criteria for both B-ALL and NHL:

• Eastern Cooperative Oncology Group performance status score of 0 or 1.

• An estimated life expectancy of at least 12 weeks according to the investigator's judgment.

• Seronegative for human immunodeficiency virus antibody (i.e., intact immune function).

• Participant has adequate bone marrow, renal, hepatic, pulmonary, and cardiac function defined as:

∙ Estimated glomerular filtration rate (eGFR) \>30 mL/min/1.73 m2 (calculated using the CKD-EPI equation \[Levey et al, 2009\]). For participants receiving an LD regimen that contains 4 days of Fludarabine, an eGFR \>=60 mL/min/1.73 m2 (calculated using the CKD-EPI equation) is required. If there is a concern that eGFR calculation is not an accurate reflection of renal function, a 24-hour urine collection for creatinine clearance may be used at the investigator's discretion.

‣ Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) levels both ≤3 times of upper limit of normal (ULN), unless there is suspected disease in the liver.

‣ Total bilirubin \<2.0 mg/dL, except in participants with Gilbert's syndrome.

‣ Platelet count ≥50,000/μL and absolute neutrophil count of ≥1000/ μL. Platelet transfusions within 14 days of screening are not allowed except for participants in B-ALL disease cohort with extensive bone marrow disease burden, in which case adequate bone marrow recovery after prior treatment is required to be documented. NHL participants with a platelet count \<50,000/μL and absolute neutrophil count (ANC) of \<1000/ μL may be enrolled with Medical Monitor approval if there is documentation of significant bone marrow involvement by disease and in the Investigator's assessment, no other reasonable etiology for the low counts.

‣ Left ventricular ejection fraction \>45% as assessed by echocardiogram (ECHO) or multiple gated acquisition scan performed within 1 month before starting lymphodepleting chemotherapy. ECHO results performed within 6 months before Screening and at least 28 days after the last cancer treatment may be acceptable if the participant has not received any treatment with cardiotoxicity risks.

‣ No clinically significant evidence of pericardial effusion or pleural effusion causing clinical symptoms and needing immediate intervention, based on the investigator's opinion. Any known effusion must be stable without need for drainage within 2 weeks of enrollment.

‣ No clinically significant renal/pulmonary comorbidities.

‣ Baseline oxygen saturation \>92% on room air.