That same lander (Chang'e 4) also measured the radiation dose rate on the moon. It's about 2.6x that of the ISS. Doesn't account for solar particle events, which they didn't encounter any.
https://www.science.org/doi/10.1126/sciadv.aaz1334 ("First measurements of the radiation dose on the lunar surface")
- "LND measured an average dose equivalent of 1369 μSv/day on the surface of the Moon."