This happens in the viewport as well as the renders.
The characters are imported from Poser, so they are not indigenous to maya.
I cannot find anything different between the connections and a Maya setup's connections, except for:
Poser: The ffd node is connected to polyShape.inmesh through a group Parts node,
Maya: The ffd node is connected directly to the polyShape.inmesh.
I re-did this to match the maya setup (and several other things) but it didn't correct the problem.
It still happens when delete the lattice joint deformers, or when I rotate the lattice.
Any ideas on what would cause the light not to update on deformations would be appreciated!