Depending on the render engine, there should be an auto LOD system that uses tessellation to work, so the animation would work normally. i think all big engines have a auto LOD system, or you can manually set the LOD meshes and the engine will do the vertex weighting automatically.
Why dont you simply bind your LODs to the same rig (skeleton) and export them separately (if there is no engine specific workflow for that) You should be able to transfer the skinweights from highrez to LOD easily (easy f.e. in Maya but also in Max, from what i hear)