Phase I/II Open-label Study Evaluating The Safety And Efficacy of Concomitant Administration of Anti-CD19 CAR T-cell Therapy and Lenalidomide in Refractory/Relapsed Chronic Lymphocytic Leukemia Patients.

Inclusion Criteria: * Documented CD19+ CLL or SLL * Patients must have failed at least 1 prior regimen * Patients must be currently receiving ibrutinib for at least 3 months prior to enrollment in the study and: * Not experiencing any ≥ grade 2 non-hematologic ibrutinib-related toxicity * ECOG Performance status 0 or 1 * 18 years of age and older * Adequate organ system function including: Creatinine \< 1.6 mg/dl ALT/AST \< 3x upper limit of normal Total Bilirubin \<2.0 mg/dl with the exception of patients with Gilbert syndrome; patients with Gilbert syndrome may be included if their total bilirubin is ≥ 3.0 x ULN and direct bilirubin ≤ 1.5 x ULN. * Have no active GVHD and require no immunosuppression * Are more than 6 months from transplant * No contraindications for leukapheresis * Left Ventricular Ejection fraction \>50% * Gives informed consent Exclusion Criteria: * CLL patients with known or suspected transformed disease (i.e. Richter's transformation). * Pregnant or lactating women. * Uncontrolled active infection. * Active hepatitis B or hepatitis C infection. * Concurrent use of systemic steroids or chronic use of immunosuppressant medications. * Any uncontrolled active medical disorder * HIV infection. * Patients with active CNS involvement with malignancy. * Class III/IV cardiovascular disability according to the New York Heart Association Classification. * Subjects with clinically apparent arrhythmia or arrhythmias who are not stable