This randomized phase II/III trial studies how well whole-brain radiation therapy works and compares it with or without hippocampal avoidance in treating patients with small cell lung cancer that is found in one lung, the tissues between the lungs, and nearby lymph nodes only (limited stage) or has spread outside of the lung in which it began or to other parts of the body (extensive stage). Radiation therapy uses high energy x-rays to kill tumor cells and shrink tumors. The hippocampus is part of the brain that is important for memory. Avoiding the hippocampus during whole-brain radiation could decrease the chance of side effects on memory and thinking. It is not yet known whether giving whole-brain radiation therapy is more effective with or without hippocampal avoidance in treating patients with small cell lung cancer.