This study enrolls patients with newly diagnosed differentiated thyroid cancer (papillary thyroid cancer or follicular thyroid cancer) that has spread to the lungs and has a genetic mutation called and NTRK fusion. The study involves taking a study drug called larotrectinib for approximately 6 months prior to receiving radioiodine therapy (RAI). The overall goal of this study is to find out if taking the study drug before RAI works better than receiving RAI alone (the usual standard of care treatment).