I believe the thickness of lead required for any significant protection would make the weight of the helmet unreasonable. Unless the exercise you mentioned consist only of weighted neck curls.

A more realistic approach to mitigating the issue is in my opinion to have rotating crews. They would spend most of their time in underground shelters, and only some minor fraction of their time doing surface work. Advances in medicine, specifically in regard to cancer, along with minimizing exposure time, is what I believe will make the risk low enough to be within acceptable bounds.