Lenvatinib and Iodine Therapy in Treating Patients With Radioactive Iodine-Sensitive Differentiated Thyroid Cancer

PRIMARY OBJECTIVE: I. To evaluate the efficacy of lenvatinib pretreatment along with radioactive iodine (RAI) in patients with previously treated RAI sensitive thyroid cancer. SECONDARY OBJECTIVES: I. To demonstrate the safety of the combination of lenvatinib and RAI in patients with Iodine sensitive differentiated thyroid carcinoma (DTC). II. To assess dynamic changes in established serum based biomarkers of DTC (thyroglobulin \[Tg\] and Tg antibody). III. To explore the utility of protein and genetic biomarkers to predict treatment efficacy. OUTLINE: Patients receive lenvatinib orally (PO) once daily (QD) for 8 weeks and up to 12 weeks in the absence of disease progression or unaccepted toxicity. Patients also receive iodine I-131 PO daily as standard of care. After completion of study treatment, patients are followed up within 6 weeks, every 3 months for 1 year, and then periodically thereafter.