The Randomization Phase will consist of a Treatment Period and a Follow-up Period. It will begin at the time of randomization of the first participant and will consist of 28-day blinded study treatment cycles. The End of Study will occur at the end of the Randomization Phase, which is defined as when the last participant enrolled completes the Week 24 tumor assessments or discontinues study treatment if before Week 24. Participants will be randomly assigned to treatment with 1 of 2 blinded dosages of lenvatinib in a 1:1 ratio to receive lenvatinib 18 mg, or 24mg orally once daily (QD). Dose reductions will occur in succession based on the previous dose level (24, 20, 14, 10, and 8 mg QD, or 18, 14, 10, 8, and 4 mg QD, respectively). Once the dose has been reduced, it may not be increased at a later date.