There are some works on doing this directly e.g. https://arxiv.org/abs/2601.23065 but getting accurate materials is a challenge for anything more than diffuse.

AI-based relighting will no doubt start working soon.

out of the box, I imagine that surfaces can be lit, but probably not shadowed correctly. (structures aren’t solids, more like particles in 3d space)

it could look like the real-time lighting of an old game engine on rather modern assets. (quake 2-3 era)

or perhaps some "occlusion pre-pass" could be done to create a voxelized sparse volume from the splats that set a "voxel opacity value" for each to absorb light? (not far from how prebaked GI works nowadays)

note: not an expert on rendering, just a nutjob that did stuff in opengl in the old days.