This phase I trial studies the side effects and best dose of genetically modified T-cells following peripheral blood stem cell transplant in treating patients with recurrent or high-risk non-Hodgkin lymphoma. Giving chemotherapy before a stem cell transplant helps stop the growth of cancer cells. When the healthy stem cells from a donor are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells. Removing the T cells from the donor cells before transplant may stop this from happening. Giving an infusion of the donor's T cells (donor lymphocyte infusion) later may help the patient's immune system see any remaining cancer cells as not belonging in the patient's body and destroy them (called graft-versus-tumor effect)

PRIMARY OBJECTIVES:

I. To assess the safety and describe the full toxicity profile of cellular immunotherapy utilizing ex vivo expanded autologous central memory T cell (Tcm)-enriched T cells that are genetically modified using a self-inactivating (SIN) lentiviral vector to express a costimulatory cluster of differentiation (CD)19-specific chimeric antigen receptors (CAR) as well as a truncated human epidermal growth factor receptor (EGFR) (CD19R:CD28 zeta/EGFR tau +Tcm) (CD19-CAR-specific/truncated EGFR lentiviral vector-transduced autologous T cells) in conjunction with a standard myeloablative autologous hematopoietic stem cell transplant (HSCT) for patients with high-risk intermediate grade B-lineage non-Hodgkin lymphoma (e.g., diffuse large B-cell lymphoma [DLBCL], mantle cell lymphoma [MCL] or transformed non-Hodgkin lymphoma [NHL]).

II. To determine the maximum tolerated dose (MTD) based on dose limiting toxicities (DLTs).

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 peripheral blood as a surrogate for the in vivo effector function of transferred autologous CD19R:CD28 zeta/EGFR tau +Tcm.

OUTLINE: This is a dose-escalation study of CD19-CAR-specific/truncated EGFR lentiviral vector-transduced autologous T cells. Patients undergo mobilization for autologous stem cell collection with cytoreductive chemotherapy and filgrastim and/or plerixafor per current standard operating policies. Patients undergo myeloablative conditioning regimen per institutional standards beginning day -7 followed by hematopoietic stem cell transplantation on day 0. Patients receive CD19-CAR-specific/truncated EGFR lentiviral vector-transduced autologous T cells IV on day 2 or 3 (may be delayed up to day 45 if the patient is not yet eligible). Patients who experience disease progression and have not experienced DLTs at greater than or equal to 100 days post HSCT will be allowed to receive an optional second T cell infusion.

After completion of study treatment, patients are followed up weekly for 1 month, monthly for 1 year, and then yearly for 15 years.

Inclusion Criteria:

• Research participants enrolled are patients with an indication to be considered for HSCT, who are diagnosed with intermediate grade B-cell NHL (e.g., DLBCL, MCL or transformed NHL), and that have either recurrence/progression following prior therapy, or verification of high-risk disease in first remission
• Karnofsky performance status of >= 70% and a 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 the history of intermediate grade B-cell NHL (e.g., DLBCL, MCL or transformed NHL)
• Negative serum pregnancy test for women of childbearing potential
• Research participant has an indication to be considered for autologous stem cell transplantation
• All patients must have the ability to understand and the willingness to sign a written informed consent

ELIGIBILITY TO UNDERGO AUTOLOGOUS MYELOABLATIVE TRANSPLANTATION WITH HEMATOPOETIC PROGENITOR CELL (HPC)A RESCUE

• Research participant meets all standard clinical parameters for candidates of autologous transplant as described in the current COH Hematopoietic Cell Transplant Standard Operating Policies, Procedures and Protocols
• Patient Evaluation & Selection or Deferral for hematopoietic cell transplantation (HCT)
• Research participant is scheduled to receive a standard chemotherapy-based conditioning regimen, such as cyclophosphamide, carmustine, etoposide (CBV) or carmustine, etoposide, cytarabine, melphalan (BEAM)
• Research participant has a cryopreserved unselected HPCA product of at least 3 x 10^6/kg CD34+ cells
• Research participant does not have evidence of disease progression after salvage therapy

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

• Research participant has a released cryopreserved T cell product
• Research participant has undergone an autologous HPC(A) procedure
• Not requiring supplemental oxygen or mechanical ventilation, oxygen saturation of 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 - Total bilirubin =< 5.0
• Research participant without clinically significant encephalopathy/new focal deficits
• No clinical evidence of uncontrolled active infections process

Exclusion Criteria:

• Research participants with any uncontrolled illness including ongoing or active infection; research participants with known active hepatitis B or C infection; research participants who are human immunodeficiency virus (HIV) seropositive based on testing performed within 4 weeks of enrollment; research participants with any signs of 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
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to cetuximab
• Research participants with known brain metastases (central nervous system [CNS] involvement or parenchymal or leptomeningeal involvement)
• Research participants with presence of other malignancy or history of prior malignancy within 5 years of study entry; although patients treated with curative intent within 5 year are eligible; this exclusion rule does not apply to non-melanoma skin tumors and in-situ cervical cancer
• Failure of research participant to understand the basic elements of the protocol and/or the risks/benefits of participating in this phase I/II 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
• 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