Cediranib Maleate With or Without Lenalidomide for the Treatment of Thyroid Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed papillary, follicular, papillary/follicular variant or Hurthle cell carcinoma; patients must be felt to be poor candidates for or refractory to further surgery or radioactive I-131 therapy; I-131 therapy must have been completed at least 4 weeks prior to enrollment; all patients are expected to be on thyroxine suppression therapy * Patients must have radiographically measurable disease; radiographically measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \> 20 mm with conventional techniques or as \> 10 mm with spiral computed tomography (CT) scan; lesions in previously irradiated anatomic areas (external beam radiation) cannot be considered target lesions unless there has been documented growth of those lesions after radiotherapy * Patients must have evidence of disease progression (20% objective growth of existing tumors by Response Evaluation Criteria in Solid Tumors \[RECIST\] criteria) within the last 12 months * In the Phase I portion, there is no limit on prior systemic therapies (cytotoxic or targeted therapies); however, patients who have discontinued previous vascular endothelial growth factor (VEGF) inhibitors secondary to adverse events are not eligible; in the Phase 2 portion, patients cannot have received more than 1 prior chemotherapy (cytotoxic or targeted) regimen; prior VEGF-pathwa…