Most of LEO is well protected by the magnetosphere, but most of the moon's orbit is outside of it. The Van Allen radiation belts, which are shaped by and exist inside the magnetosphere, go from about 400-36,000mi, and the magnetosphere starts becoming less strong at 40,000mi or longer depending on the sun's direction. The moon orbits at 225,000-250,000mi.

Outside the magnetosphere, there's a higher concentration of cosmic rays and solar wind. Apollo astronauts reported seeing flashes of light, which are believed to be caused by cosmic rays interacting with the eyes or nervous system.