Please see http://www.babylonjs-playground.com/#2QEFG#4 , where I've reproduced my problem.
I have a skybox, ground, and sphere. I've set the renderingGroupId on the skybox to 0, and the renderingGroupId on the ground and sphere to 1.
That works fine, but when I simplify the sphere (autoLOD), it appears the simplified meshes are set to renderingGroupId 0, not renderingGroupId 1 (per the parent mesh/sphere).
Thanks for your help.