Trial of CUDC-907 in Children and Young Adults With Relapsed or Refractory Solid Tumors, CNS Tumors, or Lymphoma

Inclusion Criteria: * Age \> 1 years and ≤ 21 years at time of enrollment. * Karnofsky performance status ≥ 50% for patients ≥16 years of age and Lansky ≥ 50% for patients \<16 years of age (see Appendix A) * Diagnosis requirement * For Parts A and B, participants must have evaluable or measurable disease (see Section 11). * For Part A, participants must have histologically confirmed solid tumors, CNS tumors, or lymphoma based upon biopsy or surgery at initial diagnosis and/or relapse/progression. The only exception to histologic confirmation is for pediatric tumors that are routinely diagnosed exclusively by standard clinical imaging criteria: diffuse intrinsic pontine glioma and optic pathway glioma. * For Part B, participants must have one of the following diagnoses histologically confirmed: * Neuroblastoma with evidence of Mycn/Myc positivity based on any of the following: * MYCN amplification (\> 4 copy amplification) from COG reference laboratory or other CLIA-certified laboratory; or * Mycn protein expression \> 1+ according to validated assay in Children's Hospital Los Angeles (CHLA) Clinical Pathology Laboratory; or * Myc expression \> 1+ according to validated assay in CHLA Clinical Pathology Laboratory. * One of the following mature B cell lymphoma diagnoses: * Diffuse large B cell lymphoma * Burkitt lymphoma * Participants must have disease that is relapsed or refractory and for which standard curative or palliative measures do not exist or are no longer effective. * Patients must have fully recovered from the acute toxic effects of all prior anti-cancer therapy except organ function as noted in Section 3.1.6). Patients must meet the following minimum washout periods prior to enrollment: * Myelosuppressive chemotherapy: At least 14 days after the last dose of myelosuppressive chemotherapy (42 days for nitrosourea or mitomycin C). * Radiotherapy: * At least 14 days after local palliative XRT (small port); * At least 90 days must have elapsed after prior TBI, craniospinal XRT or if \>50% radiation of pelvis; * At least 42 must have elapsed if other substantial BM radiation; * At least 42 days must have passed since last MIBG or other radionuclide therapy. * Small molecule biologic therapy: At least 7 days following the last dose of a biologic agent. For agents with known adverse events occurring beyond 7 days, this duration must be extended beyond the time in which adverse events are known to occur. If extended duration is required, this should be discussed and approved by the study chair. * Monoclonal antibody: At least 21 days after the last dose of anitbody * Myeloid growth factors: At least 14 days following the last dose of long-acting growth factor (e.g. Neulasta) or 7 days following short-acting growth factor. * Stem Cell Infusion or Cellular Therapies: The patient must have no evidence of graft versus host disease and at least 42 days must have elapsed after transplant, stem cell infusion, or cellular therapy. * Major Surgery: At least 3 weeks from prior major surgical procedure. Note: Biopsy and central line placement/removal are not considered major. * PI3K and HDAC inhibitors: The patient must not have received prior CUDC-907 therapy. Prior treatment with individual PI3K or HDAC inhibitors is allowed. Patients must not have received therapy with the combination of PI3K and HDAC inhibitors. * Participants must have normal organ function as defined below. * Bone Marrow Function: * Absolute neutrophil count ≥1,000/uL * Platelets ≥75,000/uL and transfusion independent, defined as not receiving a platelet transfusion for at least 5 days prior to CBC documenting eligibility. * Hepatic Function: * Total bilirubin ≤ 1.5 x upper limit of normal for age * ALT (SGPT) ≤ 135 U/L For the purpose of this study, the ULN for ALT is 45 U/L * Serum albumin \> 2 g/dL * Renal Function: --A serum creatinine based on age/gender as follows: Age Maximum Serum Creatinine (mg/dL) Male Female 1. to \< 2 years 0.6 0.6 2. to \< 6 years 0.8 0.8 6 to \< 10 years 1 1 10 to \< 13 years 1.2 1.2 13 to \< 16 years 1.5 1.4 ≥ 16 years 1.7 1.4 OR --Creatinine clearance ≥ 70 mL/min/1.73 m2 for participants with creatinine levels above institutional normal. * Adequate Cardiac Function: QTc \< 480 msec * Adequate GI Function: Diarrhea \< grade 2 by CTCAE version 4 * Adequate Metabolic Function: Fasting glucose \< grade 2 (\< 160 mg/dL or \< 8.9 mmol/L) without the use of antihyperglycemic agents. * Additional Agent-Specific Requirements * Patients must be able to swallow either intact capsules or mini-tabs without chewing. * In order to limit dose deviations due to rounding, patients must have a body surface area of at least 0.5 m2 * For patients with CNS tumors (primary or metastatic), any baseline neurologic deficits (including seizure) must be stable for at least one week prior to study enrollment. * Ability to understand and/or the willingness of the patient (or parent or legally authorized representative, if minor) to provide informed consent, using an institutionally approved informed consent procedure. Exclusion Criteria: * Patients must not be receiving any of the following concomitant medications: * Pharmacologic doses of systemic corticosteroids unless for CNS metastatic or primary disease. For patients with CNS metastatic or primary tumors receiving corticosteroids, they should be on a stable or decreasing dose over the 7 days prior to registration and meet criteria. * For all patients, receipt of systemic physiologic replacement steroids, topical and/or inhaled corticosteroids is acceptable. * Non-steroidal anti-inflammatory drugs, oral anticoagulants, and therapeutic heparins. * Pregnant participants will not be entered on this study given that the effects of CUDC-907 on the developing human fetus are unknown. * Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with CUDC-907, breastfeeding mothers are not eligible. * Participants of child-bearing or child-fathering potential must agree to use adequate contraception (hormonal birth control; intrauterine device; double barrier method; or total abstinence) throughout their participation, including up until 30 days after last dose of CUDC-907. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to CUDC-907. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. Note that patients who have had prior allogeneic transplantation are required to have CMV PCR testing performed during screening. A positive screen would be evidence of an active infection and would render the patient ineligible. * Patients with a known history of HIV, hepatitis B, and/or hepatitis C (testing not required as part of screening). * Patients with a known history of type 1 or type 2 diabetes mellitus. * Patients with gastrointestinal disease or disorder that could interfere with absorption of CUDC-907, such as bowel obstruction or inflammatory bowel disease.