This phase III trial compares standard therapy given after surgery (adjuvant) to standard therapy given before and after surgery (perioperative) in treating patients with stage II-IIIB non-small cell lung cancer (NSCLC) that can be removed by surgery (resectable). The usual approach for patients with resectable NSCLC is chemotherapy and/or immunotherapy before surgery, after surgery, or both before and after surgery. This study is being done to find out which approach is better at treating patients with lung cancer. Treatment will be administered according to the current standard of care at the time of enrollment. Chemotherapy options may include cisplatin, carboplatin, pemetrexed, gemcitabine, docetaxel, and vinorelbine at standard doses according to the treating physician. Cisplatin is in a class of medications known as platinum-containing compounds. It works by killing, stopping or slowing the growth of tumor cells. Carboplatin is in a class of medications known as platinum-containing compounds. It works in a way similar to the anticancer drug cisplatin, but may be better tolerated than cisplatin. Carboplatin works by killing, stopping or slowing the growth of tumor cells. Pemetrexed is in a class of medications called antifolate antineoplastic agents. It works by stopping cells from using folic acid to make deoxyribonucleic acid (DNA) and may kill tumor cells. Gemcitabine is a chemotherapy drug that blocks the cells from making DNA and may kill tumor cells. Docetaxel is in a class of medications called taxanes. It stops tumor cells from growing and dividing and may kill them. Other chemotherapy drugs, such as vinorelbine, work 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 . Immunotherapy with monoclonal antibodies, such as nivolumab, pembrolizumab, and atezolizumab, may help the body's immune system attack the tumor, and may interfere with the ability of tumor cells to grow and spread. Starting treatment with chemotherapy and immunotherapy prior to surgery and continuing treatment after surgery may be a more effective treatment option than adjuvant therapy alone in patients with stage II-IIIB resectable NSCLC.