This phase I trial studies the highest possible dose of memory enriched T cells that can be given following standard stem cell transplant before unmanageable side effects are seen in patients with B-cell non-Hodgkin lymphoma that has returned after previous treatment. A T cell is a type of immune cell that can recognize and kill abnormal cells of the body. Memory enriched T cells will be made from a patient's own T cells that are genetically modified in a laboratory. This means that the T cells are changed by inserting additional pieces of deoxyribonucleic acid (genetic material) into the cell to make it recognize and kill lymphoma cells. Memory enriched T cells may kill the cells that are not killed by stem cell transplant and may lower the chances of the cancer recurring.

PRIMARY OBJECTIVES: I. To assess the safety and determine the maximum tolerated dose (MTD) of each cellular immunotherapy product, cluster of differentiation (CD)19R (EQ) 28 zeta/truncated human epidermal growth factor receptor (EGFRt) + central memory T cell (Tcm) (Arm 1) and CD19R(EQ)28zeta/EGFRt+ naive memory T cell (TN/MEM) (Arm 2), in conjunction with a standard myeloablative autologous hematopoietic stem cell transplant (HSCT) for patients with high-risk intermediate or high grade B-lineage non-Hodgkin lymphomas.

SECONDARY OBJECTIVES: I. To determine the tempo, magnitude, and duration of engraftment of the transferred T cell product as it relates to the number of cells infused.

II. To study the impact of this therapeutic intervention on the development of normal CD19+ B-cell precursors in the bone marrow as a surrogate for the in vivo effector function of transferred autologous CD19R(EQ)28zeta/EGFRt+ Tcm or TN/MEM.

OUTLINE: This is a dose-escalation study. Patients are assigned to 1 of 2 arms. ARM 1: Patients receive autologous CD19CAR-CD28-CD3zeta-EGFRt-expressing TCM-enriched T cells intravenously (IV) over 10 minutes on day 2 or 3 following HSCT. ARM 2: Patients receive autologous CD19CAR-CD28-CD3zeta-EGFRt-expressing TN/MEM-enriched T cells IV over 10 minutes on day 2 or 3 following HSCT. Patients who experience disease progression and have not experienced serious treatment-related toxicities at greater than or equal to 100 days post T cell infusion will be allowed to receive an optional second T cell infusion.

After completion of study treatment, patients are followed up within 18-24 hours, then 18-72 hours, weekly for 1 month, monthly for 1 year, at 18, 24, and 36 months, and then annually thereafter for a minimum of 15 years.

Inclusion Criteria:

• Research participants enrolled are patients with an indication to be considered for HSCT, who are diagnosed with intermediate or high grade B-cell non-Hodgkin lymphoma (NHL) (e.g. diffuse large B-cell lymphoma [DLBCL], mantle cell lymphoma [MCL], or transformed NHL), and that have either (1) recurrence/progression following prior therapy, or (2) verification of high-risk disease in first or subsequent remission
• Karnofsky performance status (KPS) of >= 70% at time of enrollment
• Life expectancy >= 16 weeks at time of enrollment
• Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control or abstinence) prior to study entry and for six months following duration of study participation; should a woman become pregnant or suspect that she is pregnant while participating on the trial, she should inform her treating physician immediately
• City of Hope (COH) pathology review confirms that research participant's diagnostic material is consistent with history of intermediate or high grade B-cell NHL (e.g., DLBCL, MCL, or transformed NHL)
• Negative serum pregnancy test for women of child-bearing potential
• Research participant has an indication to be considered for autologous stem cell transplantation
• All subjects must have the ability to understand and the willingness to sign a written informed consent

ELIGIBILITY CRITERIA AT TIME OF INFUSION OF GENETICALLY MODIFIED AUTOLOGOUS T CELLS:

• Research participant has a released cryopreserved T cell product
• Research participant did not have evidence of disease progression after salvage therapy and therefore underwent an autologous myeloablative transplantation with hematopoietic progenitor cell autologous (HPC[A]) rescue procedure
• Not requiring supplemental oxygen or mechanical ventilation, oxygen saturation 90% or higher on room air
• Not requiring pressor support, not having symptomatic cardiac arrhythmias
• Lack of acute renal failure/requirement for dialysis, as evidenced by creatinine < 1.6 mg/dL
• Total bilirubin =< 5.0 mg/dL
• Research participant without clinically significant encephalopathy/new focal deficits
• No clinical evidence of uncontrolled active infectious process

Exclusion Criteria:

• Research participants with any uncontrolled illness including ongoing or active infections; research participants with known active hepatitis B or C infection; research participants who are human immunodeficiency virus (HIV) positive based on testing performed within 4 weeks of enrollment; research participants with any signs or symptoms of active infection, positive blood cultures or radiological evidence of infections

• Research participants receiving any other investigational agents, or concurrent biological, chemotherapy, or radiation therapy

• Research participants with a history of allergic reactions attributed to compounds of similar chemical or biological composition to cetuximab

• Research participants with known brain metastases (central nervous system [CNS] involvement either parenchymal or leptomeningeal involvement)

• Research participants with presence of other active malignancy; however, research participants with history of prior malignancy treated with curative intent and in complete remission are eligible

• Failure of research participant to understand the basic elements of the protocol and/or the risks/benefits of participating in this phase I study; a legal guardian may substitute for the research participant

• History of allogeneic HSCT or prior autologous HSCT

• Any standard contraindications to myeloablative HSCT per standard of care practices at COH

• Dependence on corticosteroids

  • Defined as doses of corticosteroids of greater than or equal to 5 mg/day of prednisone or equivalent doses of other corticosteroids
  • Note: topical and inhaled corticosteroids in standard doses and physiologic replacement for subjects with adrenal insufficiency are allowed

• Currently receiving another investigational agent

• Active autoimmune disease requiring systemic immunosuppressive therapy

• Research participants will be excluded, who in the opinion of the investigator, may not be able to comply with the safety monitoring requirements of the study