Testing the Addition of an Anti-cancer Drug, Entinostat, to the Usual Chemotherapy and Immunotherapy Treatment (Atezolizumab, Carboplatin and Etoposide) for Previously Untreated Aggressive Lung Cancer That Has Spread

This phase I trial seeks to find out the best dose, possible benefits and/or side effects of entinostat in combination with atezolizumab, carboplatin and etoposide for the treatment of previously untreated aggressive lung cancer that has spread (extensive-stage small cell lung cancer). Entinostat and etoposide may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Immunotherapy with monoclonal antibodies, such as atezolizumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Carboplatin is a chemotherapy drug that attaches to deoxyribonucleic acid (DNA) and may kill tumor cells. Giving entinostat in combination with atezolizumab, carboplatin and etoposide may work better than atezolizumab, carboplatin and etoposide alone.