Additional Study Information: This trial studies the side effects of pembrolizumab with or without chemotherapy in treating patients with non-small cell lung cancer that has come back and has spread to other places in the body. Pembrolizumab is an immunotherapy that may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Chemotherapy works in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving pembrolizumab with or without chemotherapy may shrink the tumor in older patients with non-small cell lung cancer.