Study of Volasertib and Belinostat in Patients With Relapsed and Refractory Aggressive B-cell and T-cell Lymphomas

Inclusion Criteria: A patient must meet all of the following inclusion criteria to be eligible to participate in the study. * Histologically confirmed aggressive B-cell or T-cell lymphoma including the following: * B-cell lymphomas * DLBCL (including transformed follicular lymphoma) * Mantle cell lymphoma * Burkitt lymphoma * Peripheral T-cell lymphoma (PTCL) excluding cutaneous T-cell lymphoma * Disease that is relapsed or refractory after a minimum of 2 previous therapies, if B-cell lymphoma, or a minimum of 1 previous therapy, if PTCL * For patients who have had autologous stem cell transplant, disease relapse must be more than 100 days following transplant. * For patients who have had allogeneic stem cell transplant, all of the following conditions must be met: * ≥ 6 months since allogeneic transplant * Graft vs. host disease (GVHD) is not present * Patient is not currently on immunosuppressive therapy * At least one site of measurable disease by PET/CT: a node measurable in 2 diameters and with longest diameter \>1.5cm or an extranodal lesion measurable in 2 diameters and with longest diameter \>1cm. * Age ≥ 18 years of age * Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2 (see Appendix 1) * Life expectancy of at least 3 months * CBC with differential providing evidence of adequate bone marrow function as defined below: * Absolute neutrophil count (ANC) ≥ 1500/mm3 without growth factor support for 7 days * Platelets ≥ 75,000/mm3 (without transfusion for 7 days) * Adequate renal function defined as: Creatinine ≤ 1.5 x upper limit of normal (ULN) or calculated or actual creatinine clearance ≥ 60 mL/min (see Appendix 2 for the Cockcroft -Gault Formula to calculate creatinine clearance) * Adequate hepatic function as defined below: * AST ≤ 2.5 x ULN * ALT ≤ 2.5 x ULN * Total bilirubin ≤ 1.5 mg/dL * Note: Patients with documented Gilbert's syndrome are eligible if total bilirubin is ≤ 3.0 mg/dL. * Serum potassium and serum magnesium within normal limits Note: Electrolytes may be corrected with supplementation. * For a woman of childbearing potential (WCBP), a negative serum pregnancy test performed within 14 days prior to study enrollment (7 days prior to initiation of study treatment) Note: WCBP is defined as any woman who has not had a hysterectomy or bilateral oophorectomy and is not postmenopausal (i.e., she has had menses in the preceding 24 consecutive months) * WCBP and male patients must agree to use a highly effective method of birth control for the duration of study treatment and for 6 months following completion of study treatment Note: A highly effective method of contraception is defined as one that results in a low failure rate (i.e. less than 1% per year) when used consistently and correctly, such as implants, injectables, combined oral contraceptives, some intrauterine devices (IUDs), sexual abstinence or vasectomised partner. * Ability to understand and willingness to sign a written informed consent document Exclusion Criteria: A patient who meets any of the following exclusion criteria is ineligible to participate in the study. * Any investigational treatment within 30 days prior to initiation of study treatment * Plans for concurrent treatment with other investigational agents * Plans for other concurrent cancer treatment including steroids for cancer control * Chemotherapy or large field radiotherapy within 3 weeks prior to initiation of study treatment * Previous histone deacetylase inhibitor administered as cancer treatment. * History of brain metastasis including leptomeningeal metastasis * QTc interval ≥450 (i.e., ≥ grade 0, per CTCAE version 4) on ECG prior to initiation of study treatment. If baseline QTc on screening ECG is ≥ 450 ms (i.e., ≥ grade 1) * Check potassium and magnesium serum levels * Correct any identified hypokalemia and/or hypomagnesemia and repeat ECG to confirm QTc interval * For patients with baseline HR \< 60 or \> 100 bpm, manual read of QT by cardiologist is required, with Fridericia correction applied to determine the QTcF interval. * Note: For patients with HR 60-100 bpm, no manual read of QTc is required. * Any of the following related to risk of torsades de pointes and sudden cardiac death: * History of sustained ventricular tachycardia (VT, ventricular fibrillation (VF), torsades de pointes, or resuscitated cardiac arrest unless currently addressed with an implanted cardiac defibrillator * Concomitant treatment with an anti-arrhythmic agent to prevent or control arrhythmia. Agents used for rate-control of atrial fibrillation are permitted provide that they are not prohibited due to potential drug interactions (see Section 6.4) * Known congenital long QT syndrome * Second degree atrioventricular (AV) block type II, third degree AV block, or ventricular rate \< 50 bpm * Any of the following related to ischemic heart disease: * Angina with ordinary physical activity * Note: If angina only occurs with strenuous, rapid, or prolonged exertion, the patient is eligible. * Myocardial infarction within 6 months prior to study enrollment * Note: If myocardial infarction occurred within 6-12 months prior to study enrollment, patient must be asymptomatic and have had a negative cardiac risk assessment (e.g., treadmill stress test, nuclear medicine stress test, or stress echocardiogram) * ECG with evidence of cardiac ischemia (i.e., ST depression of ≥ 2 mm, measured from isoelectric line to ST segment; T-wave inversion ≥ 4 mm measured from isoelectric line to peak of T-wave) * Any of the following related to heart failure: * New York Heart Association (NYHA) class II, III or IV congestive heart failure (see Appendix 3) or known left ventricular ejection fraction \< 40% by MUGA scan or \< 50% by echocardiogram or MRI * Known hypertrophic cardiomegaly or restrictive cardiomyopathy * Clinically significant infection including active hepatitis B or hepatitis C requiring treatment * Known human immunodeficiency virus (HIV) seropositivity nNote: HIV testing is not required * History of allergic reactions attributed to compounds similar to the chemical or biologic composition of belinostat or volasertib * History of another primary malignancy, excluding non-melanoma skin cancer, cervical carcinoma in situ, and/or other in situ cancers treated by local excision, that has not been in remission for at least 2 years * Pregnancy or breastfeeding * Medical, psychological, or social condition that, in the opinion of the investigator, may increase the patient's risk, interfere with the patient's participation in the study, or hinder evaluation of study results