Dose Escalation Study of CLR 131 in Children, Adolescents, and Young Adults With Relapsed or Refractory Malignant Tumors Including But Not Limited to Neuroblastoma, Rhabdomyosarcoma, Ewings Sarcoma, and Osteosarcoma

Inclusion Criteria: All Patients * Previously confirmed (histologically or cytologically) pediatric solid tumor (e.g., neuroblastoma, sarcoma), lymphoma (including Hodgkin's lymphoma), or malignant brain tumors that are clinically or radiographically suspected to be relapsed, refractory, or recurrent for which there are no standard treatment options with curative potential. Note: patients with diffuse intrinsic pontine glioma (DIPG) may enroll without histological or cytological confirmation. * ≥ 2 years of age and ≤ 25 years of age at time of consent/assent * If ≥ age 16 years, Karnofsky performance status of ≥ 60. If \< age 16 years, Lansky performance status ≥ 60 * Platelets ≥ 75,000/µL (last transfusion, if any, must be at least 1 week prior to study registration, and, unless deemed medically necessary, no transfusions are allowed between registration and dosing) * Absolute neutrophil count ≥ 750/µL * Hemoglobin ≥ 8 g/dL (last transfusion must be at least 1 week prior to study registration, and, unless deemed medically necessary, no transfusions are allowed between registration and dosing) * Using the bedside Schwartz formula, estimated GFR (creatinine clearance) \> 60 ml/min/1.73m2 * Alanine aminotransferase \< 3 × ULN * Bilirubin \< 2 × ULN * Patients who have undergone autologous or allogeneic bone marrow transplant must be at least 3 months from transplant. * Patients enrolling at total dose levels \> 30 millicurie (mCi)/m2 must have availability or ability to collect an autologous hematopoietic stem cell back-up product prior to CLR 131 administration. At minimum, 2 x 10\^6/kg cryopreserved CD34+ cells must be available. * Patient or his or her legal representative is judged by the Investigator to have the initiative and means to be compliant with the protocol. Patients with Pediatric Solid Tumor or Lymphoma * At least 1 measurable lesion with longest diameter of at least 10 mm. Patients with a lesion(s) that are determined to be Metaiodobenzylguanidine (MIBG) or positron emission tomography (PET) positive may be enrolled at the investigator's discretion, even if not associated with a measurable lesion of at least 10 mm. Patients with neuroblastoma who have detectable disease may enroll provided they meet the requirements of the International Neuroblastoma Response Criteria. * Patients with known brain metastases must have completed any radiotherapy or systemic treatments for brain metastases prior to enrollment; by investigator assessment be considered stable with no new signs or symptoms for at least 1 month, and on a stable dose of steroids (unchanged for three weeks prior to registration or on a steroid tapering regimen). Patients with Recurrent or Refractory Brain Tumors * At least 1 measurable lesion with longest diameter of at least 10 mm on any imaging sequence. * Patients with previously known neurological deficits must be clinically stable at time of enrollment and able to complete all study related procedures. Patients with documented or newly diagnosed neurological deficits will be enrolled at the investigator's discretion. * If patient receives steroids for neurological symptom control, the dose must be stable (unchanged for three weeks prior to registration) or on a steroid tapering regimen. Initiation of steroids per routine care immediately prior to CLR 131 dosing is acceptable. Exclusion Criteria: * Patients receiving active treatment for central nervous system metastases or those that are likely to require active treatment during anticipated participation in this trial. Patients with stable brain metastases treated with steroids may enroll at the investigator's discretion * For solid tumor and lymphoma patients only, central nervous system involvement unless previously treated with surgery, systemic therapy, or radiotherapy with the patient neurologically stable. Patients with metastatic brain tumors that have been previously treated are allowed, provided the patient is neurologically stable (determined at the investigator's discretion). * Antitumor therapy or investigational therapy, within 2 weeks of dosing. For certain types of radiation (craniospinal, total abdominal, whole lung \[spot irradiation to skull-based metastases is not considered craniospinal radiation for the purposes of this study\]), at least 3 months must have elapsed. No washout is required for palliative focal radiation. NOTE: Patients participating in non-interventional clinical trials (i.e., non-drug) are allowed to participate in this trial * Patients previously treated with iodine-131 (131I)-MIBG who have already received a cumulative I-131 dose \> 54 mCi/kg or who would exceed 54 mCi/kg by participating in this trial, are not eligible.