This phase II trial studies how well anti-cluster of differentiation (CD)19 monoclonal antibody MOR00208 and lenalidomide work in treating patients with relapsed, refractory, or previously untreated chronic lymphocytic leukemia, small lymphocytic lymphoma, or prolymphocytic leukemia. Monoclonal antibodies, such as anti-CD19 monoclonal antibody MOR00208, can block cancer growth in different ways. Some block the ability of cancer to grow and spread. Others find cancer cells and help kill them or carry cancer-killing substances to them. Biological therapies, such as lenalidomide, may stimulate the immune system in different ways and stop cancer cells from growing. Giving anti-CD19 monoclonal antibody MOR00208 and lenalidomide may kill more cancer cells.