This works as expected for me in Firestorm. High LOD file has 4 triangles with 4 materials, called "mat0" to "mat3", with the white mat3 face "hidden" under the other 3. Low LOD file has the first 3 triangles and their assigned material slots deleted, leaving a single triangle with "mat3" assigned to it.
I have no idea why it would be failing for you, perhaps the uploader log can give some insight into what's wrong (materials on a lower LOD must be a subset of the preceding one, so it's okay to have faces 0, 1, 2 and 3 on highest LOD, faces 0 and 3 on the next LOD, and face 3 on the last LOD, but it is *not* okay to go from, say, 0, 1, 2, 3 to 0, 3 to 0, 1: 0, 1 is not a subset of 0, 3.