This clinical trial is focused on studying a type of lung cancer known as metastatic non-small cell lung cancer (NSCLC). This is a condition where cancer cells have spread from the lungs to other parts of the body. The study is comparing the effects of two different treatments. One treatment combines two medications: pembrolizumab (also known by its code name MK-3475) and lenvatinib (code name MK-7902). The other treatment uses a medication called docetaxel. Pembrolizumab is given as an infusion, which means it is delivered directly into the bloodstream through a vein, while lenvatinib is taken as a capsule by mouth. Docetaxel is also given as an infusion.

The purpose of the study is to compare how well these treatments work in helping patients live longer and in slowing down the progression of the cancer. Participants in the study will receive either the combination of pembrolizumab and lenvatinib or docetaxel. The study will monitor the participants over a period to see how the cancer responds to the treatments and to check for any side effects. The study aims to provide valuable information on which treatment might be more effective for patients who have already been treated with other therapies, including chemotherapy and immunotherapy.

Throughout the study, participants will undergo regular check-ups and tests to track their health and the status of their cancer. These tests may include imaging scans like MRI or CT scans, which help doctors see inside the body and assess the size and spread of the cancer. The study will also look at the quality of life of participants, considering factors like pain and physical functioning. This research is important for finding better ways to treat metastatic NSCLC and improve outcomes for patients with this challenging condition.