Cord Blood Natural Killer (NK) Cells in Leukemia/Lymphoma

Central Venous Catheter: The chemotherapy, some of the other drugs in this study, and the NK cells will be given by vein through your central venous catheter (CVC). A CVC is a sterile flexible tube and needle that will be placed into a large vein while you are under local anesthesia. Blood samples will also be drawn through your CVC. The CVC will remain in your body during treatment. Your doctor will explain this procedure to you in more detail, and you will be required to sign a separate consent form. NK Cell Dose Levels: You will be assigned to a dose level of NK cells based on when you joined this study. Up to 5 dose levels of NK cells will be tested. The first group of participants will receive the lowest dose level. Each new group will receive a higher dose than the group before it, if no intolerable side effects were seen. This will continue until the highest tolerable dose of NK cells is found. If not enough NK cells can be produced in the laboratory for your assigned dose level, you will still receive the NK cells that were produced. If you are infused with a lower number of NK cells than had been originally planned, the CLL may not respond. Researchers do not know what number of NK cells is needed for a response. Chemotherapy and NK Cell infusion: The days before you receive the NK cells are called minus days. The day you receive the NK cells is called Day 0. The days after you receive the NK cells are called plus days. You will receive 1 of 3 study drug plans. Your doctor will decide which plan you will receive based on your age, prior treatment, diagnosis, and health status. You will receive 1 of the 3 options as explained below. Option #1: On Day -2 through Day +14, you will take lenalidomide by mouth once a day at about the same time each day. If you are able to do so, you will take aspirin or another drug as instructed by your doctor on these days to help prevent blood clots. You will be asked to complete a study drug diary and bring it to each study visit. The study staff will tell you more about this. On Day -5, you will receive fludarabine by vein over 1 hour and cyclophosphamide by vein over 3 hours. If you have a B-cell cancer, you will receive rituximab by vein over 3-6 hours. Rituximab and fludarabine are given to treat the cancer and lower the immune system in order to lower the risk of the body rejecting the NK cells. Cyclophosphamide is given to lower the immune system in order to lower the risk of graft-versus-host disease (GVHD -- when transplanted immune tissue, such as cord blood NK cells, attacks the tissues of the recipient's body). On Day -4 and -3, you will receive fludarabine by vein over 1 hour and cyclophosphamide by vein over 3 hours. On Days -2 and -1, you will rest. On Day 0, you will receive NK cells by vein. Option #2: On Day -2 through Day +14, you will take lenalidomide by mouth once a day at about the same time each day. If you are able to do so, you will take aspirin or another drug as instructed by your doctor on these days to help prevent blood clots. You will be asked to complete a study drug diary and bring it to each study visit. The study staff will tell you more about this. On Day -6, you will receive fludarabine by vein over 1 hour. Fludarabine is given to treat the cancer and lower the immune system in order to lower the risk of the body rejecting the NK cells. On Day -5, and -4, you will receive fludarabine by vein over 1 hour and cyclophosphamide by vein over 3 hours. Cyclophosphamide is given to lower the immune system in order to lower the risk of graft-versus-host disease (GVHD -- when transplanted immune tissue, such as cord blood NK cells, attacks the tissues of the recipient's body). On Day -3 and -2, you will receive fludarabine by vein over 1 hour. Fludarabine is given to treat the cancer and lower the immune system in order to lower the risk of the body rejecting the NK cells. On Day -1, you will rest. On Day 0, you will receive NK cells by vein. Option #3: On Day -7, you be given fluids by vein to hydrate you. On Days -6 through - 2, you will receive fludarabine by vein over 1 hour and cytarabine by vein over 1 hour. On Day -2 through Day +14, you will take lenalidomide by mouth once a day at about the same time each day. If you are able to do so, you will take aspirin or another drug as instructed by your doctor on these days to help prevent blood clots. You will be asked to complete a study drug diary and bring it to each study visit. The study staff will tell you more about this. On Day -1, you will rest. On Day 0, you will receive NK cells by vein. Starting on Day +5, you will receive filgrastim as an injection under the skin 1 time a day until your blood cell levels return to normal. Filgrastim is designed to help with the growth of white blood cells. Study Visits: Within 7 days before starting chemotherapy: * You will have a physical exam. * Blood (about 2 tablespoons) will be drawn for routine tests. Within 2 days and then about 1 week, 2 weeks, 3 weeks, 1 month, 2 months, 3 months, and 4 months after the NK cell infusion, the following tests and procedures will be performed: °Blood (about 4 tablespoons) will be drawn for routine tests, tests to measure levels of certain proteins, to learn how your body's immune system responds to the NK cell infusion, and to check the level of the NK cells. About 1 week, 3 weeks, 1 month, and 4 months after the NK cell infusion, you will have a bone marrow biopsy/aspiration to check the status of the disease. To collect a bone marrow biopsy/aspirate, an area of the hip or chest bone is numbed with anesthetic, and a small amount of bone and bone marrow is withdrawn through a large needle. Pregnancy Tests: If you can become pregnant, blood (about 1 teaspoon each time) will be drawn for a pregnancy test within 10-14 days and 24 hours before you are prescribed lenalidomide, at about Day +21, at 2 months after NK cell infusion, and then again 4 weeks after therapy is stopped. To continue on this study, you must not be pregnant. If possible, the blood needed for pregnancy tests will be collected during the above blood draws so that no additional needle sticks will be needed. Length of Study: You will be on study for up to about 1 year. You may be taken off study early if the disease gets worse, if you are unable to receive the NK cell infusion, if you have any intolerable side effects, if you are unable to follow study directions, if your doctor thinks it is in your best interest, if the study is stopped, or if you choose to leave the study early. You should talk to the study doctor if you want to leave the study early. If you are taken off study early, you still may need to return for routine post-transplant follow-up visits, if your doctor decides it is needed. If you are thinking about dropping out of this study, please tell the study doctor. The doctor can tell you about the effects of stopping treatment. You and the doctor can talk about what follow-up care and testing would help you the most. If you leave the study, your test results and information cannot be removed from the study records.