I have been fighting with the LOD order myself, and finally, figured it out. You have to add the empty and the LOD meshes to a new collection and it will fix the LODIndex for them. GOD, it took forever to figure that out. No documentation I could find said anything about that. I had about given up and noticed the only difference between mine and Enlightened was the collection and thought I may as well try it.
Selected the empty and the LOD Meshes, right-clicked on them, and selected “New Collection”. Reselected the empty and meshes after they moved to the collection and exported them. Told UE4 to reimport the mesh and boom order fixed. WTH.