Genetically Modified T-cell Infusion Following Peripheral Blood Stem Cell Transplant in Treating Patients With Recurrent or High-Risk Non-Hodgkin Lymphoma

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)

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