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