This phase I/II trial tests the safety and efficacy of split-course adaptive radiation therapy in combination with immunotherapy with or without chemotherapy for the treatment of patients with stage IV lung cancer or lung cancer that that has spread to nearby tissue or lymph nodes (locally advanced). Radiation therapy is a standard cancer treatment that uses high energy rays to kill cancer cells and shrink tumors. Split-course adaptive radiation therapy uses patient disease response to alter the intensity of the radiation therapy. Immunotherapy with monoclonal antibodies such as pembrolizumab, ipilimumab, cemiplimab, atezolizumab or nivolumab may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Chemotherapy drugs like carboplatin, pemetrexed, and paclitaxel work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving split-course adaptive radiation therapy with standard treatments like immunotherapy and chemotherapy may be more effective at treating stage IV or locally advanced lung cancer than giving them alone.

This phase II trial tests how well cemiplimab works in treating basal cell carcinoma of the head and neck that has spread to nearby tissue or lymph nodes (locally advanced) before surgery (neoadjuvant). Cemiplimab is a human recombinant monoclonal IgG4 antibody that may allow the body's immune system to work against tumor cells. Giving cemiplimab before surgery may make the tumor smaller and make it easier to remove.