Yeah the biggest aspects of the TK army are fear and magic. The fear is somewhat lessened by our cold blooded, which is great, but their magic is extreme. Not so powerful, but completely relentless.
The heirophant is indeed the key; not only does he make the army crumble he is part of their crucial magic. Just remember for the TK it isn't the general so they can still use general's leadership for those crumble tests and often will survive not too badly.
Focus on killing the priests, the saurus will have no trouble munching skeletons in combat but yes be careful of your flanks. You need to destroy the entire unit rather than breaking them. Ushabti are pretty powerful, chariot units are powerful but fragile, carrion are crazy with a potential 40" charge when boosted by magic. Be very careful of lone characters if they are buzzing around. Also the scorpions are quite nasty.
Overall LM shouldn't have too much trouble with TK unless he is a really awesome general, they are an army that takes much skill to master.