Liothyronine in Combination With BIT Regimen for Medulloblastoma With or Without Minimal Residual Disease

Inclusion Criteria: 1. Phase 1 and Phase 2, Cohort 1: Participants must have histologically confirmed medulloblastoma that is relapsed/progressive following standard upfront therapy. Tissue confirmation of medulloblastoma diagnosis is required at diagnosis and not required at the time of relapse for entry into the study. 2. Phase 2, Cohort 2: Participants must have cerebrospinal fluid (CSF) with cell-free deoxyribonucleic acid (cf-DNA) + assessed in a Chemiluminescent immunoassay (CLIA)-certified or protocol-approved laboratory. After entry into the study, another CSF sample will be collected and analyzed centrally prior to initiation of protocol therapy to verify cf-DNA positivity. 3. Evidence of Disease: Phase 1 and Phase 2, Cohort 1: Participants may have either Measurable or Evaluable Disease Measurable Disease: Participants must have clear residual disease at the time of enrollment, defined as tumor that is measurable in two perpendicular dimensions on MRI Evaluable Disease: Diffuse leptomeningeal disease OR clear MRI evidence of disease that may not be measurable in two perpendicular dimensions. Phase 2, Cohort 2: For cf-DNA positive cohort: Participants are not required to have measurable or evaluable disease but must have cf-DNA positivity in a CLIA-certified or protocol-approved laboratory, as above. 4. Prior Therapy: Participants must have received standard upfront therapy for medulloblastoma (either with craniospinal radiation or high dose chemotherapy and autologous stem cell rescue. If other therapy utilized, must be discussed with study chairs prior to participation). Participants for Phase 1 and Phase 2 cohort 1 may have received further chemotherapy and/or radiation therapy beyond standard upfront therapy prior to trial enrollment. Participants within the Phase 2 cohort 1 must have experienced at least one, and at most, two relapses prior to study enrollment. 5. Age 1-25 years old. 6. Performance Score: Karnofsky ≥ 50 for participants \> 16 years of age and Lansky ≥ 50 for participants ≤16 years of age (See Appendix A). Participants who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score. 7. For those participants currently treated with levothyroxine (Synthroid) they must have stable dosing for a minimum of 3 months prior to enrollment. 8. Organ Function Requirements 1. Peripheral absolute neutrophil count (ANC) ≥ 1000/cubic millimeters (mm3) 2. Platelet count ≥ 75,000/microliter (uL) (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment). 3. A serum creatinine \< 1.5 institutional/reference range upper Limit normal (ULN) based on age and gender 4. Total bilirubin ≤ 3 x upper limit of normal (ULN); in presence of Gilbert's syndrome, total bilirubin ≤ 6 x ULN or direct bilirubin ≤ 3 x ULN * Alanine aminotransferase (ALT) ≤ 5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST) ≤ 5 x ULN. 3.3.7.4 Adequate Neurologic Function Defined as: * Participants with seizure disorder may be enrolled if well controlled. Participants on non-enzyme inducing anticonvulsants may be excluded pending interaction(s) with study drug. 3.3.7.5 Adequate Cardiac Function Defined as: * Normal left ventricular systolic function on baseline transthoracic echocardiogram (TTE) * Normal left ventricular systolic function is defined as left ventricular ejection fraction (LVEF) \>55% or shortening fraction (SF) \>28%. AND * No clinically significant arrhythmia on baseline ECG (sinus arrhythmia, sinus tachycardia, sinus bradycardia, early repolarization and 1st degree atrioventricular block when partial response (PR) interval \< 300 millisecond (ms) are not considered clinically significant arrhythmias). * In addition, the following ECG findings are not considered clinically significant in the setting of a normal echocardiogram: * Left axis deviation * Left atrial enlargement * Right atrial enlargement * Possible left ventricular hypertrophy * Possible right ventricular hypertrophy * Non-specific T wave abnormality 3.3.7.6 For the Phase 1 cohort, normal adrenal axis function is required. For those participants in the Phase 2 cohort, must have controlled adrenal insufficiency \>3 months (no change in steroid replacement or stress dose plan for at least 3 months). * Normal adrenal axis function as defined as: * Morning (AM) cortisol \>11mcg/deciliter (dL) * If AM cortisol is \<11 microgram (mcg)/dL, cosyntropin stimulation test with rise to \>18 9. Endocrine conditions: Participants with diabetes insipidus, diabetes melitus, or being treated with levothyroxine, must have stable dosing and control for minimum of 3 months prior to enrollment 10. For Cohort 1 only: participants must have recovered from any surgical procedure before enrolling on this study (see below for examples of major, intermediate, and minor surgical procedures): 1. Participants with a major surgical procedure within 28 days prior to enrollment should be excluded. 2. Participants with an intermediate surgical procedure within 14 days prior to enrollment should be excluded. 3. For minor surgical procedures (including Broviac line or infusaport placement), participants should not receive the first planned dose of bevacizumab until the wound is healed and at least 7 days have elapsed. 4. There should be no anticipation of need for major surgical procedures during the course of the study. 11. The effects of L-T3 with chemotherapy on the developing human fetus are unknown. For this reason and because chemotherapy agents as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entr