This study is for participants that have been diagnosed with small cell lung cancer, that has spread to the brain. The purpose of this study is to see if high dose radiation therapy delivered only to the small areas of brain cancer and avoiding the surrounding normal brain tissue, called stereotactic radiosurgery (SRS), decrease side effects related to memory and thinking compared to radiation to the entire brain, called, whole-brain radiation therapy (WBRT) that avoids the hippocampus but treats all of the brain tissue along with a drug that helps preserve memory and thinking called memantine. Participants can expect to be on this study for up to 6 months, depending on what treatment they receive (SRS alone or HA-WBRT with memantine). Participants will then be followed every 2 to 3 months for at least 1 year after study completion and then every 6 months for their lifetime or until disease progression.