Phase II Palbociclib +Ibrutinib in Mantle Cell Lymphoma

Inclusion Criteria: 1. Subjects must have histologically or cytologically confirmed MCL as defined by the World Health Organization. All patients must have either t(11;14) by karyotype or fluorescent in-situ hybridization (FISH) or positive immunohistochemistry (IHC) for cyclin D1. 2. Subjects must have measurable disease defined as at least one tumor lesion of at least 1.5 cm by CT or MRI, PET positive lesion(s) or a peripheral blood CD5+, CD19+ lymphocyte count of at least 5,000 cells/µL. 3. Subjects must have received at least one prior systemic therapy. 4. Subjects who have received prior autologous stem cell transplant are eligible. Patients that have undergone prior allogeneic stem cell transplant will only be eligible if the patient is no longer taking immunosuppressive therapy and there are no significant ongoing transplant-related adverse effects. 5. Subjects must be age ≥ 18 years 6. ECOG performance status ≤ 2 7. Patients must have normal organ and marrow function as defined below: 8. Laboratory Values: * ANC ≥ 1000 cells/μL, unless bone marrow involvement in MCL, then ANC \>500 cells/μL; * Platelets ≥ 75,000 cells/μL, unless bone marrow involvement in MCL, then platelets \>30,000 cells/μL; * Calculated creatinine clearance ≥30mL/min; * AST or ALT ≤ 2.5x ULN; * Total bilirubin ≤ 1.5x ULN; * QTc ≤ 480 ms 9. Subjects must be able to provide written, informed consent 10. Subjects must have recovered from adverse events to ≤ grade 1 from prior therapies 11. Subjects must be able and willing to swallow and retain oral medication without a condition that would interfere with enteric absorption 12. Subjects may be receiving prednisone at a maximum dose of 20 mg orally daily for symptom control. 13. Serum or urine pregnancy test must be negative within 7 days of starting study treatment in women of childbearing potential. Women of childbearing potential and men with female partners who are able to become pregnant are required to use a highly effective form of barrier contraception for the duration of the study and for 90 days after the last dose of study drug. Adequate contraception is defined as abstinence or two forms non hormonal contraception, which is a combination of two forms of the following: * Condom with spermicidal foam/gel/cream/suppository * occlusive cap (diaphragm or cervical vault caps) with spermicidal * non hormonal intrauterine device (IVD) 14. No evidence of active hepatitis B or C infections (i.e., no positive serology for anti-HBc or anti-HCV antibodies) 15. HBV seropositive patients (HBsAg +) are eligible if they are closely monitored for evidence of active HBV infection by HBV DNA testing and receive suppressive therapy with lamivudine or other HBV suppressive therapy until 6 months after the last rituximab dose. 16. Patients with HIV infection are eligible, provided they meet the following: * No evidence of coinfection with hepatitis B or C * CD4+ cell count ≥ 400/mm3 * No evidence of resistant strains of HIV * If not on anti-HIV therapy, HIV viral load \< 10,000 copies HIV RNA/mL If on anti-HIV therapy, HIV viral load \< 50 copies HIV RNA/mL * No history of AIDS-defining conditions * No use of strong CYP3A4/5 inhibitors or inducers Exclusion Criteria: 1. Subjects that have received prior CDK4/6 inhibitor will not be eligible. 2. Subjects that have received any prior BTK inhibitor \> 90 days prior to enrollment will not be eligible. 3. Subjects with known or suspected CNS involvement. 4. Concurrent therapy with other investigational products. 5. History of allergic reactions attributed to compounds of chemical or biologic composition similar to palbociclib. 6. Subjects receiving any medications or substances that are strong or moderate inhibitors or strong inducers of CYP3A isoenzymes within 7 days of starting study treatment (See Appendix II). 7. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, diabetes, or psychiatric illness/social situations that would limit compliance with study requirements. 8. Subjects with myocardial infarction within 6 months prior to enrollment or has New York Heart Association (NYHA) Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities are not eligible. Prior to study entry, any ECG abnormality at screening has to be documented by the investigator as not medically relevant. 9. Pregnant women, or women of childbearing potential without a negative pregnancy test (serum or urine) within 7 days prior to registration, irrespective of the method of contraception used, are excluded from this study because the effect of palbociclib on a developing fetus is unknown. Breastfeeding should be discontinued prior to study entry. 10. Subjects must agree to use barrier contraceptive methods throughout the study period up until at least 90 days post last palbociclib dose. 11. Subjects with clinically significant history of liver disease, including viral or other known hepatitis, current alcohol abuse, or cirrhosis, etc. 12. Subjects with another active malignancy that limits survival. 13. Subjects with a bleeding diathesis are not eligible. 14. Subjects with transfusion-dependent thrombocytopenia are not eligible.