Donor Natural Killer Cell Infusion, Rituximab, Aldesleukin, and Chemotherapy in Treating Patients With Relapsed Non-Hodgkin Lymphoma or Chronic Lymphocytic Leukemia

Inclusion Criteria: * Patient 18 years or older with a diagnosis of non-Hodgkin Lymphoma or chronic lymphocytic leukemia (NHL or CLL) and one of the following: * Progression of NHL following at least 2 prior chemotherapy regimens, (must contain rituximab for all NHL and fludarabine for follicular NHL) defined as: * failure to achieve partial remission (PR) with the last chemotherapy * disease progression within 6 months following last chemotherapy * Progression of CLL/SLL (small lymphocytic lymphoma) following at least 2 prior chemotherapy regimens (containing purine analogs ) in stage Rai III or IV or symptomatic disease. * Relapsed NHL or CLL following stem cell transplantation for whom the option of donor lymphocyte infusion is not available or clinically indicated (e.g. recipients of autologous or umbilical cord blood \[UCB\] transplants). * Available related HLA-haploidentical (human leukocyte antigen) natural killer (NK) cell adult donor by at least Class I serologic typing * Karnofsky performance status \> 60% * Measurable disease based on modified Response Evaluation Criteria In Solid Tumors (RECIST) * Have acceptable organ function as defined within 28 days of enrollment: * Hematologic: platelets ≥ 80,000 x 10\^9/L; hemoglobin ≥ 9g/dL, unsupported by transfusions; absolute neutrophil count (ANC) ≥ 1000 x 10\^9/L, unsupported by granulocyte-colony stimulating factor or granulocyte-macrophage colony-stimulating factor (G-CSF or GM-CS)F for 10 days or Neulasta for 21 days - the hematologic requirements are waived for patients with inadequate counts due to known bone marrow involvement by lymphoma who are otherwise eligible * Renal: glomerular filtration rate (GFR) \> 50 ml/min * Hepatic: alanine aminotransferase (ALT), aspartate aminotransferase (AST) \< 3 x upper limit of normal and total bilirubin \<3 mg/dl * Pulmonary function: \>50% corrected carbon monoxide diffusing capacity (DLCO) and Forced Expiratory Volume in the first second (FEV1) * Cardiac: no symptoms of uncontrolled cardiac disease, left ventricular ejection fraction \>40% * Off prednisone or other immunosuppressive medications for at least 3 days prior to Day 0 * Women of childbearing potential must agree to use adequate contraception (diaphragm, birth control pills, injections, intrauterine device \[IUD\], surgical sterilization, subcutaneous implants, or abstinence, etc.) for the duration of treatment. * Voluntary written informed consent before performance of any study-related procedure not part of normal medical care. Exclusion Criteria: * Pregnant or lactating. The agents used in this study may be teratogenic to a fetus and there is no information on the excretion of agents into breast milk. All females of childbearing potential must have a blood test or urine study within 2 weeks prior to registration to rule out pregnancy. Women of childbearing age must use appropriate contraceptive method. * Active central nervous system (CNS) lymphoma/leukemia * Active serious infection (pulmonary infiltrates or lesions are allowed only after the appropriate diagnostic testing is negative for infection or appropriate therapy was initiated for probable infection) * Pleural effusion - large enough to be detectable on the chest x-ray * Allergy to rituximab or IL-2 * Human immunodeficiency virus (HIV) and associated non-Hodgkins lymphoma (NHL) * Active concurrent malignancy (except skin cancer) requiring systemic therapy in the past 2 years * Epstein-Barr virus (EBV) post-transplant lymphoproliferative disorder * Positive hepatitis B surface antigen (HBsAg). If Hepatitis B core antibody (HBcAb) is positive, Hepatitis B deoxyribonucleic acid (DNA) by polymerase chain reaction (PCR) will be evaluated. Positive anti HBcAb and undetectable viral load does not exclude the patient. * Any experimental therapy in the past 30 days Donor Selection: * Related donors (sibling, parent, offspring, parent or offspring of an HLA identical sibling) ≥ age 18 years * Able and willing to undergo lymphapheresis * HLA-haploidentical donor/recipient match. If time permits and multiple donors are available, preference will be given to the Killer-cell Immunoglobulin-like Receptors (KIR) ligand mismatched donor (as predicted by HLA typing). * HIV-1, HIV-2 negative, Human T-lymphotropic virus Type I (HTLV-1), HTLV-2 negative, West Nile virus (WNV) negative, Hepatitis B and C negative * Adequate organ function defined as: * Hematologic: CBC/diff/platelet count near normal limits, * Hepatic: ALT \< 2 x upper limit of normal, * Not pregnant or lactating * In general good health as determined by the study physician * Able to give informed consent