Aparently they had some radiation shielding, just not for the wavelengths that would need heavy lead covering.
[Aparently they had some radiation shielding](https://www.asme.org/wwwasmeorg/media/resourcefiles/aboutasme/who%20we%20are/engineering%20history/landmarks/apollobr.pdf), just not for the wavelengths that would need heavy lead covering.
They're protected against solar radiation at the very least. And possibly enough to survive the van allen belt if things went seriously wrong, I presume.