Genetically Engineered Lymphocytes, Cyclophosphamide, and Aldesleukin in Treating Patients With Relapsed or Refractory Mantle Cell Lymphoma or Indolent B-Cell Non-Hodgkin Lymphoma

Inclusion Criteria:

* Male or female subjects with immuno histopathologically documented CD20+ mantle cell lymphoma, follicular non-Hodgkin lymphoma (NHL), small lymphocytic lymphoma/chronic lymphocytic leukemia, marginal zone, or lymphoplasmacytic NHL of any age, gender, or ethnic group who have relapsed or are refractory to conventional chemotherapy and who are not eligible for Fred Hutchinson Cancer Research Center (FHCRC)/University of Washington Medical Center (UWMC) transplant protocols (or who refuse participation in transplant protocols)
* Willingness to sign an informed consent and undergo study tests
* Willingness to receive cytoreductive chemotherapy, if necessary to debulk tumors prior to T cell administration, and to receive cyclophosphamide for lymphodepletion
* Serologic evidence of prior exposure to Epstein-Barr virus (EBV)
* Meets safety criteria to undergo leukapheresis
* Hemoglobin \> 9.0 gm/dL
* White blood cell (WBC) \> 2500 per microliter
* Alanine aminotransferase (ALT) (serum glutamic pyruvate transaminase \[SGPT\]) =\< 2.5 x Upper Limit of Normal
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) =\< 2.5 x Upper Limit of Normal
* Creatinine =\< 1.6 mg/dL
* Willingness to use acceptable (barrier or hormonal methods) birth control as appropriate during the course of the study

Exclusion Criteria:

* Treatment with fludarabine or cladribine within the previous 2 years prior to apheresis
* Known central nervous system involvement with NHL
* Pulmonary involvement with NHL; a diagnosis of pulmonary lymphoma will be based in part on findings from chest computed tomography (CT) and, if clinically appropriate, lung biopsy
* Exposure to chemotherapeutic agents (standard or experimental) or other immunosuppressive therapies less than four weeks prior to apheresis; patients must have recovered from acute side effects of such therapy
* Positive serology for human immunodeficiency virus (HIV)
* Active Hepatitis B or Hepatitis C infection
* History of hypersensitivity reactions to murine proteins or seropositivity for human anti-mouse antibody (HAMA)
* Requirement for corticosteroid therapy during the study period unless used specifically for amelioration of toxicity induced by transferred cells
* Treatment with anti-CD20 antibodies (rituximab, tositumomab, ibritumomab) within 4 months prior to start of T cell infusions
* Patients with lymph nodes in excess of 5 cm in diameter at time of T cell infusion
* Patients with \> 5000 circulating CD20+ lymphocytes per mm\^3 at time of T cell infusion
* Previous allogeneic stem cell transplantation
* Life expectancy less than 90 days
* Pregnancy