Lenalidomide in Acute Leukemias and Chronic Lymphocytic Leukemia.

Inclusion Criteria:

* Blood blast count must be \< 40,000/uL prior to initiation of therapy. Hydroxyurea (up to 6g/day) may be administered prior to initiation of therapy and during the first week to maintain blood blast count \< 40,000/uL
* ECOG(Eastern Cooperative Oncology Group)performance status 0-2.
* Patients with CNS(central nervous system)involvement will be considered eligible for this study if no residual leukemic cells are detected in the CSF (cerebrospinal fluid)following intrathecal chemotherapy or radiation.

Exclusion Criteria:

* Patients with acute promyelocytic leukemia are excluded unless patient has failed salvage therapy with arsenic.
* Patients with HIV are excluded due to increased risk of infectious complications, marrow suppression, and potential interactions with antiviral therapy.
* CLL patients who have had chemotherapy (with the exception of hydroxyurea) or radiotherapy within 4 weeks prior to entering the study are excluded. CLL patients receiving corticosteroids (within 2 weeks) for treatment of disease (other than autoimmune manifestations of CLL) are not eligible.
* Patients who have received mitomycin C or nitrosourea require a six weeks recovery period before they can be enrolled on the current study.
* Patients with the following abnormal clinical values are excluded (unless abnormalities in these parameters are directly attributable to malignancy): Serum creatinine \>2.0 mg/dl Total bilirubin \> 2 x upper limit of normal (unless due to Gilbert's syndrome) ALT and AST \> 5 x upper limit of normal