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 o…