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

The goal of this clinical research study is to learn if lirilumab in combination with rituximab can help to control either CLL or Small lymphocytic lymphoma (SLL). The safety of the drug combination will also be studied.

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.

Eligibility Criteria:
Inclusion Criteria:

1. Patients will have a diagnosis of CLL or SLL who meet one or more criteria for active disease as defined by the International Working Group for CLL (IWCLL) and are: a. Cohort 1: refractory to and/or relapsed after at least one prior therapy OR b. Cohort 2: untreated patients with high-risk molecular features such as del(17p), mutated TP53, del(11q), unmutated IGHV gene, or are \>65 years of age
2. Age 18 years or older
3. Eastern Cooperative Oncology Group (ECOG) Performance Status \</=2
4. Patients must have adequate renal and hepatic function: Serum bilirubin \</=1.5 x upper limit of normal (ULN). For patients with Gilbert's disease, serum bilirubin up to \</=3 x ULN is allowed provided normal direct bilirubin; Serum creatinine ≤1.5 x ULN; alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \</=3 x ULN
5. Females of childbearing potential must have a negative serum or urine beta human chorionic gonadotrophin (Beta-hCG) pregnancy test result within 24 hours prior to the first dose of treatment and must agree to use an effective contraception method during the study and for 12 months following the last dose of the study drugs. Females of non- childbearing potential are those who are postmenopausal greater than 1 year or who have had a bilateral tubal ligation or hysterectomy. Males who have partners of childbearing potential must agree to use an effective contraceptive method during the study and for 31 weeks following the last dose of study drugs.
6. Patients or their legally authorized representative must provide written informed consent.

Exclusion Criteria:

1. Prior malignancy active within the previous 2 years except for locally curable cancers that have been apparently cured, such as basal or squamous cell skin cancer, superficial bladder cancer, carcinoma in situ of the cervix or breast, or localized prostate cancer. If patients have another malignancy that was treated within the last 2 years, such patients may be enrolled if the likelihood of requiring systemic therapy for this other malignancy within 2 years is less than 10%, as determined by an expert in that particular malignancy at MD Anderson Cancer Center and after consultation with the Principal Investigator.
2. Any major surgery, radiotherapy, chemotherapy, biologic therapy, immunotherapy, experimental therapy within 4 weeks prior to the first dose of the study drugs. For oral targeted therapies (such as ibrutinib, idelalisib, venetoclax), a washout of 3 days is allowed. Note: Prior treatment with anti CD20 monoclonal antibody, anti CD52 monoclonal antibody and lenalidomide are allowed. Prior treatment with anti-CTLA-4 and anti-PD1 therapies is allowed after a wash-out of 5 half-lives.
3. Significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 2 months of screening, or any Class 3 or 4 cardiac disease as defined by the New York Heart Association Functional Classification.
4. History of stroke or cerebral hemorrhage within 2 months.
5. Patients who have uncontrolled hypertension (defined as sustained systolic blood pressure \>/= 160 mmHg or diastolic \>/= 100 mmHg).
6. Known evidence of active cerebral/meningeal CLL. Patients may have history of central nervous system (CNS) leukemic involvement if definitively treated with prior therapy and no evidence of active disease at the time of registration.
7. Active, uncontrolled autoimmune hemolytic anemia or immune thrombocytopenia requiring steroid therapy.
8. Patients with autoimmune diseases are excluded: Patients with a history of Inflammatory Bowel Disease (including Crohn's disease and ulcerative colitis) are excluded from this study as are patients with a history of autoimmune disease (e.g., rheumatoid arthritis, systemic progressive sclerosis, systemic lupus erythematosus, Wegener's granulomatosis).
9. Patients with previous allogeneic stem cell transplant (SCT) within 6 months or with active acute or chronic graft-versus host disease are excluded. Patients must be off immunosuppression for graft versus host disease (GVHD) for at least 60 days before Cycle 1 Day 1.
10. Patients with organ allografts (such as renal transplant) are excluded.
11. History of any hepatitis (e.g., alcohol or non-alcohol steatohepatitis (NASH), auto immune, or grade 3-4 drug-related hepatitis).
12. Patients who are on high-dose steroids (doses \>10mg/day of prednisone or equivalent) or immune suppression medications. Note: Patients on high-dose steroids (doses \>10mg/day of prednisone or equivalent) or immune suppression medications are eligible provided these drugs are discontinued at least 3 days prior to starting on the study drugs.
13. Patients with uncontrolled active infection (viral, bacterial, and fungal) are not eligible.
14. Current or chronic hepatitis B or C infection, or known seropositivity for HIV.
15. Patient is pregnant or breast-feeding.
16. Concurrent use of investigational therapeutic agent
17. Patients may not receive other concurrent chemotherapy, radiotherapy, or immunotherapy. Localized radiotherapy to an area not compromising bone marrow function does not apply.
18. Other severe acute or chronic medical or psychiatric condition or laboratory abnormality that in the opinion of the investigator may increase the risk associated with study participation or investigational product administration or may interfere with the interpretation of study results and/or would make the patient inappropriate for enrollment into this study.