This trial uses a combination of two drugs, lenvatinib and pembrolizumab, to treat patients with cancer that hasn't responded to other treatments. Lenvatinib stops cancer cells from growing, while pembrolizumab helps the immune system attack the cancer. The combination received accelerated FDA approval in September 2019 for all patients with advanced endometrial cancer who have disease progression following previous treatments. The treatment cycles last a few weeks and can continue for several months unless there are side effects or other reasons to stop.