Lirilumab With Rituximab for Relapsed, Refractory or High-risk Untreated Chronic Lymphocytic Leukemia (CLL) Patients

Study Treatment: Each study cycle is 28 days. You will receive rituximab by vein over about 4-6 hours on Days 1,8, 15, and 22 of Cycle 1. After Cycle 1, you will receive rituximab on Day 1 of Cycles 2-12. You will also receive lirilumab by vein over about 1 hour on Day 1 of each cycle. Study Visits: On Days 1, 8, 15, and 22 of Cycles 1 and 2 and then about every 2 weeks during Cycles 3-6: * You will have a physical exam. You will not have this exam on Days 8 and 22 of Cycle 2. * Blood (about 2 tablespoons) will be drawn for routine tests. If the doctor thinks it is needed, more blood may need to be drawn and you may need to have these tests performed more often. The study doctor will tell you if more blood will be drawn or if you will have this blood draw repeated. On Day 1 of each cycle, if you can become pregnant, blood (about 1 tablespoon) or urine will be collected for a pregnancy test. On Day 28 of Cycles 3 and 6: * You will have physical exam. * Blood (about 2 tablespoons) will be drawn for routine tests. This routine blood draw may include a pregnancy test if you can become pregnant. Urine may also be collected for this pregnancy test. * You will have a bone marrow aspiration/biopsy to check the status of the disease. * You will have a computerized tomography (CT) or positron emission tomography (PET) scan. At least 1 time each month after Cycle 7: * You will have physical exam. * Blood (about 2 tablespoons) will be drawn for routine tests. At least 1 time every 3 months after Cycle 7: * Urine will be collected for routine tests. This routine urine collection will include a pregnancy test, if you can become pregnant. Blood (about 1 tablespoon) may also be drawn for this pregnancy test. * You will have a bone marrow aspiration/biopsy to check the status of the disease. * You will have a CT or PET scan. Any time that the doctor thinks it is needed while you are on study, you will have blood draws, CT or PET scans, and/or bone marrow aspirations/biopsies to check the status of the disease and/or to monitor your health. If the doctor thinks it is acceptable, you may be able to have some of these tests, such as routine blood and urine collections, performed at a local lab or clinic closer to your home. The results will be sent to the study doctor for review. Ask the study staff or study doctor about this possibility. Length of Study: You may receive up to 12 cycles of rituximab and up to 24 cycles of lirilumab. You will no longer be able to take the study drugs if the disease gets worse, if intolerable side effects occur, or if you are unable to follow study directions. Your participation on the study will be over after about 1 year of follow-up visits. End-of-Study Visit: Within 30 days after your last dose of study drug: * You will have a physical exam. * Blood (about 2-3 tablespoons) will be drawn for routine tests. * If the doctor thinks it is needed, you will have a bone marrow aspirate to check the status of the disease. * If the doctor thinks it is needed, you will have a CT or PET scan. Follow-Up Visits: After your end-of-study visit, you will have the following tests and procedures performed. One (1) time each month for up to 1 year: * You will have a physical exam. * Blood (about 2-3 tablespoons) will be drawn for routine tests. One (1) time every 3-6 months for up to 1 year, if the doctor thinks it is needed: * You will have a bone marrow aspirate to check the status of the disease. * You will have a CT scan or a PET scan. If you start a new type of anticancer treatment during the year after your last dose of study drugs, you will stop having these follow-up visits. This is an investigational study. Lirilumab is not FDA approved or commercially available. Rituximab is FDA approved and commercially available for the treatment of CLL. The use of these drugs in combination to treat CLL/SLL is considered investigational. The study doctor can explain how the drugs are designed to work. Up to 48 participants will be enrolled in this study. All will take part at MD Anderson.