Safety and Efficacy of Tenalisib (RP6530) in Combination With Romidepsin in Patients With Relapsed/Refractory T-cell Lymphoma

Inclusion Criteria: 1. Pathologically confirmed T-cell lymphomas at the enrolling institution. 2. Disease status as defined as relapsed or progressed patients who have received at least one systemic therapy. 3. The patients should have received NOT more than three prior systemic combination chemotherapies 4. PTCL patients must have measurable disease defined as at least one bidimensional measurable lesion with minimum measurement of \> 1.5 cm in the longest diameter. 5. Must have ECOG performance status ≤ 2 6. Adequate bone marrow, liver and renal function in line with below mentioned laboratory requirements. 1. Hemoglobin ≥8.0 g/dL 2. Absolute neutrophil count (ANC) ≥1,000/µL 3. Platelet count ≥75,000/μL 4. Total bilirubin ≤1.5 times the ULN (or ≤3 x ULN, if patient has Gilbert syndrome) 5. AST (SGOT) and ALT (SGPT) ≤ 3 x ULN; ≤ 5 ULN in case of liver involvement 6. Calculated creatinine clearance (CrCl) \> 50 ml/min by Cockcroft-Gault formula 7. Use of an effective means of contraception for women of childbearing potential and men with partners of childbearing potential. 8. Provide written informed consent prior to any study-specific screening procedures. 9. Willingness and capability to comply with the requirements of the study Exclusion Criteria: 1. Patient receiving anticancer therapy including any investigational therapy ≤3 weeks or 5 half-lives (whichever is shorter) prior to C1D1. 2. Patient who discontinued prior therapy with PI3K inhibitors or HDAC inhibitors due to drug toxicity. 3. PTCL patients with Allo-SCT on active GVHD or immunosuppression therapy within 3 months prior to C1D1. CTCL patients with the history of Allo-SCT will be excluded. 4. Patient with medical conditions requiring the use of systemic immunosuppressive medications (\> 20 mg/day of prednisone or equivalent). 5. Severe bacterial, viral or mycotic infection requiring systemic treatment. 6. Known seropositive requiring anti-viral therapy for human immunodeficiency virus (HIV) infection. 7. Known seropositive requiring anti-viral therapy for hepatitis B virus (HBV) infection OR evidence of active hepatitis B infection as defined by detectable viral load if the antibody tests are positive.. 8. Known seropositive requiring anti-viral therapy for hepatitis c virus (HCV) infection OR patients with positive hepatitis C virus Ab. 9. Subjects with active EBV unrelated to underlying lymphoma (positive serology for anti- EBV VCA IgM antibody and negative for anti-EBV EBNA IgG antibody, or clinical manifestations and positive EBV PCR consistent with active EBV infection. 10. Subject with active CMV (positive serology for anti-CMV IgM antibody and negative for anti-CMV IgG antibody and positive CMV PCR with clinical manifestations consistent with active CMV infection) and requiring therapy. 11. Uncontrolled or significant cardiovascular disease including, but not limited to: * Congenital long QT syndrome. * QTcF interval \> 450 msec * Myocardial infarction or stroke/TIA within the past 6 months * Uncontrolled angina within the past 3 months * Significant ECG abnormalities including 2nd degree atrio- ventricular (AV) block (AV) block type II, 3rd degree AV block. * History of clinically significant arrhythmias (such as ventricular tachycardia, ventricular fibrillation or torsades de pointes), * History of other clinically significant heart disease (ie, cardiomyopathy, congestive heart failure with NYHA functional classification III-IV, pericarditis, significant pericardial effusion) * Requirement for daily supplemental oxygen therapy.