Inclusion Criteria:

1. Patients must have a diagnosis of relapsed or refractory B-cell NHL:

* DLBCL, Mantle Cell, Follicular Lymphoma, Lymphoplasmacytic lymphoma, Small Lymphocytic Lymphoma, Primary Mediastinal B-Cell Lymphoma, Burkitt Lymphoma, transformed lymphoma.

* Subjects with small lymphocytic lymphoma (SLL) must have progressed after at least 2 prior therapies and prior treatment with or intolerance of both ibrutinib and venetoclax.
* Subjects with DLBCL, primary mediastinal B- Cell lymphoma, Burkitt lymphoma and transformed lymphoma must have relapsed or failed to respond to \>= 2 prior lines of multiagent chemoimmunotherapy with prior exposure to both an anti-CD20 antibody agent and an anthracycline.
* Subjects with indolent lymphomas (follicular lymphoma and lymphoplasmacytic lymphoma) must have relapsed after or been refractory to \>=2 prior lines of multi-agent chemoimmunotherapy including prior exposure to rituximab and at least 2 other chemotherapy agents.
* For subjects with Mantle cell lymphoma, previous lines of therapy may include multiagent chemotherapy including alkylating agent or anthracycline and anti CD20 antibody therapy and Bruton's tyrosine kinase (BTK) inhibitor therapy.
* Positron Emission Tomography (PET) -positive disease according to "Recommendations for Initial Evaluation, Staging, and Response Assessment of Hodgkin and Non-Hodgkin Lymphoma: The Lugano Classification"
* At least one of the following:

* Primary refractory or early relapse (first remission \< 12 months) and not eligible for stem cell transplant
* Relapsed or refractory disease after two or more lines of systemic therapy
* No significant circulating disease, defined as an elevated total lymphocyte count above the ULN due to the presence of malignant cells.
2. CD19 positive by either immunohistochemistry or flow cytometry analysis on any biopsy. If prior anti-CD19 therapy has been administered, CD19 positivity has to be re-established on the most recent biopsy.
3. Age \>=18 years at the time of consent
4. Absolute lymphocyte count \> 100/ (microliter)
5. Eastern Cooperative Oncology Group (ECOG) performance status \< 2
6. Adequate organ function, defined as:

* Adequate bone marrow function for apheresis and lymphodepleting chemotherapy

* Hemoglobin (Hgb) \>8 grams per deciliter (gm/dl) (transfusions allowed)
* Platelets \>50,000/microliter (uL) (transfusions allowed)
* Absolute Neutrophil Count (ANC) \> 500/uL
* Alanine aminotransferase (ALT)/aspartate aminotransferase (AST) \< 3 x institutional upper limit of normal (ULN) and Total bilirubin \< 1.5 mg/dl x institutional ULN, except with Gilbert's syndrome
* Serum Creatinine \< 2 x the institutional ULN
* Adequate cardiac function, defined as left ventricular ejection fraction (LVEF) \> 40% as assessed by echocardiogram or multiple uptake gated acquisition (MUGA) within 3 months of screening. Repeat testing may occur at Investigator's discretion.
7. Adequate vascular access for leukapheresis procedure (either peripheral line or surgically placed line).
8. Women of childbearing potential (defined as all women physiologically capable of becoming pregnant) must have a negative serum or urine pregnancy test AND agree to use highly effective methods of contraception for 1 year after the last dose of antiCD19 CAR-T cells
9. Males who have partners of childbearing potential must agree to use an effective barrier contraceptive method
10. Ability to understand a written informed consent document, and the willingness to sign it.

Exclusion Criteria:

1. Autologous transplant within 6 weeks of planned CAR-T cell infusion
2. Recipient of prior CAR-T cell therapy targeting CD19 outside of this protocol
3. Active other malignancy, other than non-melanoma skin cancer, carcinoma in situ (e.g., cervix, bladder, or breast).
4. HIV seropositivity
5. Serologic status reflecting active hepatitis B or C infection. Patients that are positive for hepatitis B core antibody, hepatitis B surface antigen (HBsAg), or hepatitis C antibody must have a negative polymerase chain reaction (PCR) prior to enrollment. (PCR positive patients will be excluded.)
6. Subjects with uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, pulmonary abnormalities or psychiatric illness/social situations that would limit compliance with study requirements.
7. Pregnant or breastfeeding women are excluded from this study because CAR-T cell therapy may be associated with the potential for teratogenic or abortifacient effects. Because there is an unknown, but potential risk for adverse events in nursing infants secondary to treatment of the mother with CAR-T cells, breastfeeding should be discontinued. These potential risks may also apply to other agents used in this study. NOTE: Women of childbearing potential must have a negative serum or urine pregnancy test.
8. Patients with history of clinically relevant central nervous system (CNS) pathology such as epilepsy, seizure disorders, paresis, aphasia, uncontrolled cerebrovascular disease, severe brain injuries, dementia and Parkinson's disease.
9. History of autoimmune disease (e.g., rheumatoid arthritis, systemic lupus erythematosus) with requirement of immunosuppressive medication within 6 months.
10. Body weight \<40 kilograms(kg)

Eligibility for Infusion of Investigational Product:

Subjects will undergo an evaluation of eligibility on day 1 prior to infusion of anti-CD19 CAR-T cell product. This eligibility criterion will include the inclusion and exclusion criteria required for enrollment with the following exceptions and additions:

1. No significant laboratory abnormalities. Laboratory result abnormalities that are considered not clinically significant by the principal investigator AND are not the result of a demonstrated active infection or an active central nervous system condition.
2. ECOG performance status \< 2
3. No evidence of uncontrolled intercurrent illness including, but not limited to ongoing or active infection, inflammatory response, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, pulmonary abnormalities or psychiatric illness/social situations.
4. No new neurologic symptoms suggestive of an active central nervous system condition, or uncontrolled CNS involvement by lymphoma.
5. No corticosteroid use within 7 days prior to infusion (with exception of agents used for prevention of emesis during lymphodepletive chemotherapy).