Safety and Dose Finding Study of Neratinib in Children and Young Adults With Cancer That Has Returned or Not Responded to Treatment

Inclusion Criteria: * Diagnosis: Pathologic confirmation of solid tumor, including central nervous system tumor or lymphoma. * Recurrent or Refractory Disease for which no further effective standard treatment is available. * Patient must have failed at least one prior therapy. * All patients must have evaluable disease as defined as: * Solid tumors must have a lesion evaluable by RECIST criteria version 1.1; * Central nervous system tumors will be evaluated by RANO criteria. * Available tissue to perform protein and genomic analysis * Age: * Phase 1: ≥ 3 and ≤ 21 years of age at time of enrollment * Phase 2: ≥ 3 and ≤ 21 years of age at diagnosis * Body Surface Area requirements varied by dose level: Dose Level BSA (m2) * 1 ≥ 0.82 1. ≥ 0.66 2. ≥ 0.52 3. ≥ 0.45 * Performance level: * Lansky score ≥ 60% (patients \< 16 years of age) * Karnofsky score ≥ 60% (patients ≥ 16 years of age) * Cardiac Function: Patients must have a shortening fraction ≥ 27% or left ventricular ejection fraction ≥ 50% measured by echocardiogram (ECHO) or measured by multiple-gated acquisition scans (MUGA). * Negative β-human chorionic gonadotropin (hCG) pregnancy test for female patients of child-bearing potential ≤ 7 days before starting neratinib therapy. * Female patients of reproductive potential must agree and commit to the use of a highly effective method of contraception, as determined to be acceptable by the investigator, from the time of informed consent until 28 days after the last dose of the investigational product. Male patients must agree and commit to use a barrier method of contraception while on treatment and for 3 months after the last dose of the investigational product. * Written informed consent/assent prior to any study-specific procedures. * Patient must be able to swallow tablet or have existing gastrostomy feeding tube to enable administration of tablet. * Patients must have recovered from the acute toxic effects of all prior therapy to ≤ grade 1 before entering this study. Exclusion Criteria: * Prior treatment within the following timeframes: * Systemic chemotherapy or biologic therapy ≤ 2 weeks or 5 half lives (t ½) of the agent used, whichever is shorter, prior to the start of neratinib * Radiation therapy outside the central nervous system ≤ 14 days prior to neratinib * Radiation to the central nervous system ≤ 12 weeks prior to initiation of neratinib * Patients with previous allogeneic stem cell transplant (SCT) if they meet either of the following criteria: * 60 days from allogeneic SCT * Active acute or chronic graft-versus-host-disease (GvHD) or receiving immunosuppressive therapy as treatment for GvHD * Inadequate marrow function in Cohort 1: * Absolute neutrophil count \< 1.0 x 10\^9 /L * Platelets \< 100 x 10\^9 /L * Hemoglobin \< 8.0 g/dL (transfusion permitted at least 7 days prior to baseline) * Total bilirubin \> 1.5 X the upper limit of normal (ULN) for age * AST (SGOT) and ALT (SGPT) \> 3 X ULN (unless attributed to disease involvement) * Serum creatinine \> 1.5 X ULN for age or creatinine clearance ≤ 60mL/min/1.73m\^2 * Symptomatic or unstable brain metastases. (Note: Asymptomatic patients with metastatic brain disease who have been on a stable dose of corticosteroids for treatment of brain metastases for at least 14 days (or decreasing dose of corticosteroid) are eligible to participate in the study.) Patients with primary central nervous system tumors are eligible. * Clinically active cardiac disease, including prolonged QTc interval ≥ 481ms (i.e. ≥ grade 2) * Pregnant or breast-feeding women * Being actively treated for a concurrent malignancy with the exception of basal cell carcinoma or carcinoma in situ of the cervix. * Uncontrolled intercurrent illness including, but not limited to uncontrolled infection, unexplained fever \> 38.5°C (101.3°F) or psychiatric illness/social situation that would limit compliance with study requirements. * Significant chronic gastrointestinal disorder with diarrhea as a major symptom (e.g., Crohn's disease, malabsorption, or Grade ≥ 2 National Cancer Institute \[NCI\] Common Terminology Criteria for Adverse Events Version 4.0 \[CTCAE v.4.0\] diarrhea of any etiology at baseline). * Known history of human immunodeficiency virus (HIV) infection or acquired immunodeficiency syndrome (AIDS)-related disease * Known history of hepatitis C or known active hepatitis B infection * Known hypersensitivity to any component of the investigational product