This is a multicenter, randomized, double-blind study being conducted as a postmarketing requirement to the US Food and Drug Administration (FDA) to evaluate whether there is a lower starting dosage of lenvatinib 24 mg once daily (QD) that provides comparable efficacy but has a better safety profile in participants with radioiodine-refractory differentiated thyroid cancer RR-DTC with radiographic evidence of disease progression within the prior 12 months.