I. Determine the maximum tolerated dose (MTD) of cediranib (cediranib maleate) plus lenalidomide. (Phase I) II. Determine the progression-free survival rates of single agent cediranib in patients with iodine refractory, unresectable differentiated thyroid cancer (DTC) who have evidence of disease progression within 12 months of study enrollment. (Phase II) III. Determine the progression-free survival rates of cediranib in combination with lenalidomide in patients with iodine refractory, unresectable DTC who have evidence of disease progression within 12 months of study enrollment. (Phase II) IV. Compare the progression-free survival curves of single agent cediranib to combination therapy with cediranib with lenalidomide. (Phase II)