To be fair, the shadow is present through all three levels of LOD, which is fine, as all three models will be placed in the exact same location. So, to the untrained eye, the shadow will be cast by all three LOD's.
I personally don't see an issue here.
If you were to run this test again with all three models placed int he exact same location, you wouldn't be able to tell that the shadow isn't working properly.
Cheers
Jay.