Therapeutic Effects of Epstein-Barr Virus Immune T-Lymphocytes Derived From a Normal HLA-Compatible Or Partially-Matched Third-Party Donor in the Treatment of EBV Lymphoproliferative Disorders and EBV-Associated Malignancies

Inclusion Criteria: * Pathologically documented EBV antigen positive lymphoproliferative disease, lymphoma or other EBV-associated malignancy. OR * Evaluable disease as demonstrated by clinical and/or radiologic studies with current or prior elevated blood levels of EBV DNA exceeding 500 copies/ml by quantitative real time polymerase chain reaction (PCR). OR * Persistent or recurrent elevations in levels of EBV DNA exceeding 500 copies/ml in patients previously treated for EBV-LPD with chemotherapy and/or rituximab who do not yet have clinically or radiologically evaluable disease but are at high risk of disease recurrence. * EBV-specific T cells are available for adoptive immune cell therapy from a consenting third party donor. The third party EBV-CTLs to be administered will be selected on the basis of two criteria: 1) that they are matched for at least 2 HLA antigens and 2) that they are restricted by an allele shared with the EBV+ malignancy (if known), or with the donor in HSCT recipients, or patient in organ transplant or immunodeficient patients * KPS or Lansky score ≥ 20. * A life expectancy of at least 6 weeks. * Adequate bone marrow, heart, lung, liver and kidney function at the time of treatment with EBV-specificT cells is initiated, including: 1. Absolute neutrophil count (ANC) ≥ 1,000/µL, with or without GCSF support 2. Platelets ≥ 20,000/µL 3. Creatinine ≤ 2.0mg/dl 4. Alanine aminotransferase (ALT), aspartate aminotransferase (AST) \< 3.0x and total bilirubin \< 2.5x the institutional upper limit of normal (ULN) 5. Stable blood pressure and circulation not requiring pressor support 6. Adequate cardiac function as demonstrated by EKG and/or echocardiographic evidence (may be performed within 30 days prior to treatment) * However, abnormalities of specific organs will not be considered grounds for exclusion if they are the result of the EBV+ malignancy or its treatment (e.g. a renal allograft recipient with an EBV LPD may be on dialysis because the allograft was rejected when the immune suppression was stopped as a first approach to treatment of the EBV LPD). At the discretion of the investigator, patients with elevated but stable creatinine will not be precluded from treatment on study. * There is no age restriction to eligibility for this protocol. It is expected that five types of patients afflicted with EBV-associated lymphomas, lymphoproliferative diseases or malignancies will be referred and will consent to participate in this trial. These are: 1. Patients developing EBV lymphomas or lymphoproliferative disorders following an allogeneic hematopoietic progenitor stem cell transplant (HSCT) (ie, marrow, PBSC, or umbilical cord blood). 2. Patients developing EBV lymphomas or lymphoproliferative disorders following an allogeneic organ transplant. 3. Patients with AIDS developing EBV lymphomas or lymphoproliferative diseases as a consequence of the profound acquired immunodeficiency induced by HIV. 4. Patients who develop EBV lymphomas or lymphoproliferative diseases or other EBV-associated malignancy as a consequence of profound immunodeficiencies associated with a congenital immune deficit or acquired as a sequela of anti-neoplastic or immunosuppressive therapy. 5. Patients who develop other EBV-associated malignancies without pre-existing immune deficiency, including: EBV+ Hodgkin's and Non-Hodgkin's disease, EBV+ nasopharyngeal carcinoma, EBV+ hemophagocytic lymphohistiocytosis, or EBV+ leiomyosarcoma. Exclusion Criteria: The following patients will be excluded from this study: * Patients with active (grade 2-4) acute graft vs. host disease (GVHD), chronic GVHD or an overt autoimmune disease (e.g. hemolytic anemia) requiring high doses of glucocorticosteroid (\>0.5 mg/kg/day prednisone or its equivalent) as treatment * Patients who are pregnant * Patients with severe comorbidities, not related to their EBV-associated malignancy, that would be expected to preclude their survival for the 6 weeks required to assess response of T cell therapy * Patients eligible for MSK protocol #16-803 (EBV-CTL-201)