Additional Study Information: The purpose of this study is to compare the drugs ramucirumab and pembrolizumab to standard-of-care treatment in patients whose lung cancer has progressed on immunotherapy. The study doctors hope to learn if the drug combination will help patients with stage IV or recurrent non-small cell lung cancer (NSCLC) live longer. The study is set up to find out if this drug combination is better, the same, or worse than the usual treatment. The usual approach is the care most people get for lung cancer. For patients not in a study, the usual approach is treatment with chemotherapy, which is approved by the Food and Drug Administration (FDA). Combining ramucirumab and pembrolizumab is not approved by the FDA to treat advanced lung cancer.