Study of Feasibility and Safety of UCD19 Chimeric Antigen Receptor (CAR) T Cells in Adult Subjects With Relapsed/Refractory (R/R) B-Cell Non-Hodgkin's Lymphoma (B-NHL)

Inclusion Criteria:

* Provision of signed and dated Informed Consent form.
* Stated willingness to comply with all study procedures and availability for the duration of the parent study and the long-term follow-up observational study.
* Male or non-pregnant, non-lactating females, aged 18 to 80 years.
* Performance status according to the Eastern Cooperative Oncology Group ≤ 2.
* Failed two or more lines of systemic therapy.
* Unable to receive commercially available CD19 CAR T Cells.
* Relapsed or primary refractory CD19 positive (i.e. CD19 expressing) B-NHL of the following types as confirmed by either flow cytometry, Immunohistochemistry (IHC), or both:

  * Diffuse large B-cell lymphoma (DLBCL)
  * Burkitt lymphoma
  * Intermediate lymphoma between Burkitt and DLBCL
  * Primary Mediastinal B-cell lymphoma (PMBL)
  * Follicular lymphoma
  * Mantle cell lymphoma (MCL)
  * Marginal zone lymphoma (MZL)
* No available curative alternative treatment, as determined by primary treating oncologist.
* No active Graft-versus-Host Disease (GvHD).
* In women of childbearing potential, willingness to use effective means of birth control for 1 year after UCD19 CAR T Cell infusion.

Exclusion Criteria:

* Prior therapies:

  * Received monoclonal antibody therapy within 14 days of the apheresis; or
  * Received immunomodulatory drugs (lenalidomide, tyrosine kinase inhibitors) within 14 days of the apheresis; or
  * Received corticosteroids more than 7.5mg/day within 14 days of the apheresis (physiologic replacement allowed up until apheresis, as clinically indicated); or
  * Allogeneic hematopoietic stem cell transplant with 90 days (immunosuppressive therapy for at least 4 weeks) of apheresis; or
  * Donor lymphocyte infusion within 4 weeks of apheresis.
  * Cluster of differentiation 3 (CD3) count \<0.15 x 106 cells/mL
* Severe psychiatric illness that could impede the patient's ability to provide informed consent and/or adhere to the parent protocol and/or the long-term follow-up protocol.
* Active HIV (Acquired Immune Deficiency Syndrome) or history of HIV infection, as directed by schedule or if known.
* Active Hepatitis B or Hepatitis C infection.
* Diffusion capacity of the lungs for carbon monoxide \< 40% predicted prior to lymphodepletion.
* Left ventricular ejection fraction \< 40% (evaluated by echocardiogram \[ECHO\] or Multigated Acquisition Scan \[MUGA\]) prior to lymphodepletion.
* Transaminases \> 5x upper limit of normal prior to lymphodepletion.
* Serum Bilirubin \> 4 mg/dL prior to lymphodepletion.
* Serum Creatinine \> 1.6 mg/dL or measured creatinine clearance \< 50 mL/min prior to lymphodepletion.
* Active infection that is unresponsive to antimicrobial therapy prior to lymphodepletion.
* Females planning to become pregnant during the course of the study.
* Unwillingness or inability to comply with study visits and study procedures for the entire duration of study participation.
* Unsuitable for cellular therapy for any reason, in the opinion of the Investigator.
* Any prior gene therapy, including prior CAR T cell therapy.
* Active central nervous system (CNS) disease.