Oral LBH589 in Relapsed or Refractory Chronic Lymphocytic Leukemia (CLL) and Mantle Cell Lymphoma (MCL)

Inclusion Criteria: * Ability to provide written informed consent obtained prior to participation in the study and any related procedures being performed * Patients must meet the following laboratory criteria (unless dysfunction is due to organ infiltration by lymphoma): * ANC ≥ 1.5 x 10\^9/L * Hemoglobin ≥ 9 g/dl * Platelets ≥ 75 x 10\^9/L * Calculated CrCl ≥50 mL/min (MDRD Formula) * Total serum calcium ≥ LLN * Total serum magnesium ≥ LLN * Aspartic transaminase (AST) and alanine transaminase (ALT) ≤ 2.5 x ULN * Serum bilirubin ≤1.5 x ULN * Serum potassium ≥ LLN * Thyroid stimulating hormone (TSH) ≥ lower limit of normal (LLN) and free T4 within normal limits. Patients are permitted to receive thyroid hormone supplements to treat underlying hypothyroidism. * Baseline multiple uptake gate acquisition scan (MUGA) or echocardiogram (ECHO) must demonstrate left ventricular ejection fraction (LVEF) ≥ the lower limit of the institutional normal. * Eastern Cooperative Oncology Group (ECOG) Performance Status of ≤ 2 * Documented MCL by biopsy or CLL by biopsy or flow cytometry. * Relapsed or refractory disease despite 1 or more lines of therapy. Exclusion Criteria: * Prior histone deacetylase (HDAC), DAC, HSP90 inhibitors or valproic acid for the treatment of cancer * Patients who will need valproic acid for any medical condition during the study or within 5 days prior to first LBH589 treatment * Peripheral neuropathy ≥ Common Terminology Criteria for Adverse Events (CTCAE) grade 3 * Impaired cardiac function or clinically significant cardiac diseases, including any one of the following: * Patients with congenital long QT syndrome * History or presence of sustained ventricular tachyarrhythmia. (Patients with a history of atrial arrhythmia are eligible but should be discussed with the Sponsor prior to enrollment) * History of ventricular fibrillation or torsade de pointes * Bradycardia defined as HR\< 50 bpm. Patients with pacemakers are eligible if HR ≥ 50 bpm. * Screening 12 lead electrocardiogram (ECG) with a QTc \> 450 msec * Right bundle branch block + left anterior hemiblock (bifascicular block) * Myocardial infarction or unstable angina ≤ 6 months prior to starting study drug * Other clinically significant heart disease (e.g., congestive heart failure (CHF) New York Heart Association (NYHA) class III or IV , uncontrolled hypertension, history of labile hypertension, or history of poor compliance with an antihypertensive regimen) * Impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of LBH589 * Patients with diarrhea \> CTCAE grade 1 * Other concurrent severe and/or uncontrolled medical conditions (e.g., uncontrolled diabetes or active or uncontrolled infection) including abnormal laboratory values, that could cause unacceptable safety risks or compromise compliance with the protocol * Patients using medications that have a relative risk of prolonging the QT interval or inducing torsade de pointes if treatment cannot be discontinued or switched to a different medication prior to starting study drug * Have received targeted agents within 2 weeks or within 5 half-lives of the agent and active metabolites (which ever is longer) and who have not recovered from side effects of those therapies. * Have received either immunotherapy within \< 8 weeks; chemotherapy within \< 4 weeks; or radiation therapy to \> 30% of marrow-bearing bone within \< 2 weeks prior to starting study treatment; or who have not yet recovered from side effects of such therapies. * Have undergone major surgery ≤ 4 weeks prior to starting study drug or who have not recovered from side effects of such therapy * Women who are pregnant or breast feeding or women of childbearing potential (WOCBP) not using an effective method of birth control. WOCBP are defined as sexually mature women who have not undergone a hysterectomy or who have not been naturally postmenopausal for at least 12 consecutive months (i.e., who has had menses any time in the preceding 12 consecutive months). WOCBP must have a negative serum pregnancy test within 24 hours of receiving the first dose of study medication. * Male patients whose sexual partners are WOCBP not using effective birth control * Prior malignancy within the last 5 years (except for basal or squamous cell carcinoma, or in situ cancer of the cervix) * Known positivity for human immunodeficiency virus (HIV) or hepatitis C; baseline testing for HIV and hepatitis C is not required * Significant history of non-compliance to medical regimens or unwilling or unable to comply with the instructions given to him/her by the study staff. * Have not received prior therapy for aggressive MCL or CLL. * No documentation of disease refractoriness (i.e. progression of disease despite current therapy or recurrence within 3 months of last treatment) or relapse despite prior therapy.