I have not done lithophanes but I understand they are done with translucent plastic rather than transparent.
There is an illumination technique for engraved transparent plastic where the edges are highly polished and the light source is placed so the light enters the edge. When the plastic is untouched the light reflects around inside by total internal reflection from the surface, however, if the surface is engraved the light escapes through the 'damaged' surface. Probably everyone has seen an example of this in illuminated EXIT signs.
I wonder if a lithophane in clear acrylic illuminated from the edges this way might look quite interesting. The amount of light escaping from the engraved surfaces depends to some extent on the orientation of that surface relative to the source of the light. With high intensity colored LED illumination it would be possible to have different colors come from different edges so different proportions of different colors would escape at each part of the picture. With some experimentation it might even be possible to make 'full color' lithophanes.