Dasatinib and lenalidomide are both prescribed for use in patients with different cancers of the blood. This study is experimental because neither drug has been approved by the Food and Drug Administration for the treatment of chronic lymphocytic leukemia. There are few standard treatments when fludarabine is no longer effective in patients with CLL. Some patients have received additional combination therapy with fludarabine, Campath, bone marrow transplants or supportive care. Dasatinib and lenalidomide have been effective in high-risk CLL patients in other pilot mono therapy studies. The combination of dasatinib and lenalidomide has not been studied in humans before and this study is designed to test whether this combination is safe to use.