Cord Blood Natural Killer (NK) Cells in Leukemia/Lymphoma

Inclusion Criteria:

1. Patients with history of hematologic malignancies who have received at least 2 lines of standard chemoimmunotherapy and have persistent disease.
2. Patients with acute lymphoblastic leukemia (ALL), acute myelogenous leukemia (AML), chronic myelogenous leukemia (CML) with relapsed or refractory disease who are not eligible for stem cell transplantation or other standard therapies.
3. Patients with histologically confirmed aggressive hematologic malignancies with chemotherapy-refractory disease. Chemotherapy refractory disease is defined as one or more of the following: Stable disease or progressive disease as best response to most recent chemotherapy containing regimen or disease progression or recurrence within 12 months of prior Autologous or allogeneic stem cell transplant. Subjects must have received adequate prior therapy including at a minimum: anti-CD20 monoclonal antibody unless tumor is CD20-negative, an anthracycline containing chemotherapy regimen. Subjects with transformed FL must have received prior chemotherapy for follicular lymphoma and subsequently have chemo-refractory disease after transformation to diffuse large B-cell lymphoma (DLBCL).
4. Patient with Hodgkin's Lymphoma with relapsed or refractory disease who are not eligible for stem cell transplantation or other standard therapies.
5. Patients at least 3 weeks from last cytotoxic chemotherapy. Patients may continue tyrosine kinase inhibitors and/or lenalidomide until the day of study consent.
6. Karnofsky Performance Scale \> 60%.
7. Adequate hepatic function, as defined by SGPT \<3 X upper limit of normal; serum bilirubin and alkaline phosphatase \<2 X upper limit of normal, or considered not clinically significant by the study doctor or designee, serum creatinine of \</=2 mg/dl.
8. Able to provide written informed consent.
9. 18-80 years of age.
10. All study participants must be registered into the mandatory Revlimid REMSTM program, and be willing and able to comply with the requirements of the Revlimid REMSTM program. Females of childbearing potential must adhere to the scheduled pregnancy testing and contraception as required in the Revlimid REMSTM program. A female of childbearing potential (FCBP) is a sexually mature female who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months).
11. Men must agree to use a latex condom during sexual contact with females of child bearing potential even if they have had a successful vasectomy.
12. Patients must have a CB unit available which is matched with the patient at 3, 4, 5, or 6/6 HLA class I (serological) and II (molecular) antigens.
13. Patients who are HIV positive must be willing to comply with effective antiretroviral therapy.

Exclusion Criteria:

1. Positive beta HCG in female of child-bearing potential defined as not postmenopausal for 24 months or no previous surgical sterilization or lactating females.
2. Presence of Grade 3 or greater toxicity from the previous treatment.
3. Concomitant use of other investigational agents.
4. Not consenting to participate in LAB00-099.
5. Patients with known hypersensitivity to lenalidomide and/or rituximab (CD20+ patients only).
6. Patients who are HIV positive with a detectable viral load \> 750 copies/ml on adequate retroviral therapy must be evaluated for HIV drug resistance test (HIV-1 genotype). These patients may be enrolled only after discussion with the PI and the Infectious Disease team.