Memory Enriched T Cells Following Stem Cell Transplant in Treating Patients With Recurrent B-Cell Non-Hodgkin Lymphoma

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