Microtransplantation seeks to give the participant donor cells in hopes that those cells can attack the underlying cancer. However, since the donor cells do not replace all of the host cells, it can hopefully avoid many of the serious risks involved with standard transplant, including graft-vs.-host disease (GVHD) - a complication where the donor cells attack the participant's normal body. Recent studies have suggested that lenalidomide can help aid donor cells to attack cancer when given after a stem cell transplant. This trial is trying to see if lenalidomide can help encourage the attack of leukemia cells by donor cells given as part of microtransplantation.