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

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 descr…