 This is a multicenter, randomized, double-blind, placebo-controlled Phase 3 study to compare the progression free survival of participants with 131 I -refractory DTC and radiographic evidence of disease progression within the prior 12 months, treated with lenvatinib 24 mg by continuous once daily oral dosing versus placebo. The study is conducted in 3 phases: a Prerandomization Phase screening and baseline period, a Randomization Phase double-blind treatment period, and an Extension Phase Optional Open Label OOL Lenvatinib Treatment Period and a follow-up period. 