They likely will not bother any non-moving inverts by tasting/ eating. They will usually (not always) eat your shrimp & crabs though, unless you get a very large hermit crab. Your problem may be of the indirect kind with them -- your tank will need to be big enough so that the lion's fins don't run into any stinging inverts, while a good-sized moray will knock over un-secured inverts and the small rocks they are normally attached to as the moray ventures around your tank.
Hi:
Steve is right on the money. The lions and snowflake won't be interested in non moving things. They will however prevent you from having smaller fish and moving inverts like shrimp and crabs. I consider having a lionfish in a reef to be reef-limiting but definately reefafe.
As an antecdote I have read from a few people where their lions have sampled mushroom from live rock. only to spit them out.
frank
what are the disadvantages of not having shrimp and crabs? How about snails? can i have them? The lion and the eel would be the only fish really. It's a 300 gallon system with 5"DSB and a great skimmer IMO (aerofoamer 824) so I think the nitrates would stay low.