Whoops. Just found this older post that clarifies that LB does not support Illustrator Clipping Masks: Clipping Mask Adobe Illustrator
But, linked in that post, is this article: Image Masking - LightBurn Software Documentation
showing how to use clipping masks in LB itself. So I just redid the artwork so that I’m importing the vector cut lines only, importing the rasters separately into LB, and doing all the clipping there. Works well, though it would be nice to be able to do complete artwork in Illustrator and just import/send in LB. Ah well. This way does guarantee more control for layers, I suppose.