This phase I trial studies the side effects and best dose of lenalidomide when given together with alvocidib in treating patients with relapsed or refractory B-cell chronic lymphocytic leukemia or small lymphocytic lymphoma. Lenalidomide may stop the growth of leukemia or lymphoma by blocking blood flow to the cancer. Alvocidib may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Giving lenalidomide together with alvocidib may kill more cancer cells.