Nivolumab in Epstein-Barr Virus (EBV)-Positive Lymphoproliferative Disorders and EBV-Positive Non-HodgkinLymphomas

* INCLUSION CRITERIA: * Subjects must have histologically or cytologically confirmed EBV-positive LPD or an EBV-positive NHL confirmed by the Laboratory of Pathology, NCI. * EBV-positive LPD. Subjects may be previously untreated or relapsed from prior therapy. 1. Lymphomatoid granulomatosis (LYG), grades I-II 2. Chronic active EBV disease (CAEBV) of B-cells or T-cells 3. EBV-positive post-transplantation lymphoproliferative disorder (PTLD) NOTE: PTLD after solid organ transplantation is excluded. Patients who, at the discretion of the investigator, need urgent therapy with standard agents will not be eligible. * EBV-positive B-cell NHL. Subjects must have relapsed from previous treatment with an anthracycline and rituximab-based regimen or be considered not eligible for the same. 1. Lymphomatoid granulomatosis (LYG), grade III 2. EBV-positive immunodeficiency-associated diffuse large B-cell lymphoma (DLBCL) 3. EBV-positive DLBCL * Subjects must be at least 2 weeks from prior anti-lymphoma therapy (including radiation therapy) * Subjects must be at least 100 days from prior stem cell transplant (autologous or allogeneic) or Donor Lymphocyte Infusion (DLI) * Age \>=12 years * Patients \>= 12 and \< 18 years of age should weigh at least 40 kilograms (kg); there is no weight requirement for adult subjects. * NOTE: If a pediatric patient is identified for possible enrollment who weighs less than 40 kg, the safety of the nivolumab dosing strategy used in this study must be discussed with the PI and manufacturer to confirm safety, and this discussion/approval for enrollment documented in the medical record prior to declaring the pediatric patient eligible. * Adequate performance status as follows: * Patients \>= 16 years must have ECOG Performance Status 0-2 (Karnofsky \>=60%) * Pediatric patients \< 16 years must have Lansky play-performance of 60-100% * Subjects must have measurable or evaluable disease. * Subjects must have adequate organ and bone marrow reserve (unless disease-related) as defined below: * absolute neutrophil count - \>= 750/mcL; \>= 500/mcL if impairment is due to LPD/NHL * platelets - \>= 50,000/mcL; \>= 25,000/mcL if impairment is due to LPD/NHL (transfusions not permitted) * Hemoglobin - \>= 9g/dL (transfusion permitted) * total bilirubin - \< 3.0g/dl OR \< 5.0g/dl if Gilbert s syndrome or disease infiltration of the liver is present * AST(SGOT)/ALT(SGPT) - \<= 3 X institutional upper limit of normal * serum creatinine OR creatinine clearance - Adults: \<= 1.5 mg/dL; Minors: serum Cr \<= age-adjusted normal OR \>= 40 ml/min/1.73m\^2 Age(Years) 12-15: Maximum Serum Creatinine (mg/dl): 1.2 Age(Years) \> 15: Maximum Serum Creatinine (mg/dl): 1.5 * A formalin fixed tissue block or at least 15 slides of tumor sample (archival or fresh) must be available for performance of correlative studies. NOTE: Patient must be willing to have a pre-treatment tumor biopsy if adequate archival tissue is not available. * The toxicity profile of nivolumab in patients with disease involvement of the central nervous system (CNS) is unknown. For this reason, we will introduce early stopping rules. * The effects of nivolumab on the developing human fetus are unknown. For this reason, the following measures apply: * Women of childbearing potential (WOCBP) must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) during screening and within 48 hours prior to the first dose of nivolumab. * WOCBP and men who are sexually active with WOCBP must use adequate contraception (e.g., hormonal or 2 barrier methods with a failure rate of less than 1% per year or abstinence) prior to study entry and throughout study drug administration. WOCBP receiving nivolumab will be instructed to adhere to contraception for a period of 23 weeks after the last dose of investigational product. Men receiving nivolumab and who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 31 weeks after the last dose of investigational product. * Women who are not of childbearing potential (i.e., who are postmenopausal or surgically sterile as well as azoospermic men do not require contraception). * WOCBP is defined as any female who has experienced menarche and who has not undergone successful surgical sterilization (hysterectomy, bilateral tubal ligation, or bilateral oophorectomy), and who is not postmenopausal. Post menopause is defined as: 1. Amenorrhea \>= 12 consecutive months without another cause, and a documented serum follicle stimulating hormone (FSH) level \> 35 mIU/mL or 2. Women with irregular menstrual periods and a documented serum follicle stimulating hormone (FSH) level \> 35 mIU/mL or NOTE: FSH level testing is not required for women \>= 62 years old with amenorrhea of \>= 1 year 3. Women on hormone replacement therapy (HRT) * Pregnant women are excluded from this study because nivolumab is an IgG monoclonal antibody with the potential for teratogenic or abortifacient effects. * Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with nivolumab, nursing should be discontinued if the mother is treated with nivolumab. * Ability of subject or Legally Authorized Representative (LAR) to understand and sign the written informed consent document. EXCLUSION CRITERIA: * Subjects who are receiving any other investigational agents. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to nivolumab. * Subjects with second malignancies requiring active systemic therapy are excluded. Subjects with second malignancies not requiring active systemic therapy or pre-malignant conditions such as monoclonal B-cell lymphocytosis (MBL) or monoclonal gammopathy of undetermined significance (MGUS) may be eligible. * Subjects with any condition or autoimmune disease that requires systemic corticosteroids (\> 10 mg daily prednisone equivalents) or immunosuppressive medications within 14 days of study drug administration. Inhaled or topical steroids are permitted. * Subjects with active graft-vs-host disease (GVHD) requiring steroids or other immunosuppressive agents; history of \>=grade II acute GVHD or extensive chronic GVHD. * Subjects who have had solid organ transplant. * Prior therapy with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137 or anti CTLA-4 antibody. * Non-oncology vaccine therapies for prevention of infectious disease within 4 weeks of study drug administration. * A serious uncontrolled medical condition requiring therapy. * Seizures disorder not controlled by anti-seizure medications. * Subjects with CNS involvement may be included on the study as long as they have not had any seizure activity in past 4 weeks. * Hepatitis B virus surface antigen positive. * Active Hepatitis C infection with a positive PCR; subjects who are Hepatitis C antibody positive and PCR negative may be eligible. In these cases, the subjects will be monitored via HCV PCR throughout the study. * History of anaphylactic reaction to monoclonal antibody therapy. * HIV positive subjects are excluded because the function of their T-cell immune responses is impaired.