the lobster will only eat the snail or crab if it has died. Lobsters are scavengers, and they will eat detritus and move sand for sure. Just make sure your tank is stable. And acclimate them good before dropping them in. Provide a good cave also. Someplace dark when the lights are on.
The guy I bought all my live rock from gave me a purple lobster, but his tank was a train wreck (covered in green hair algae). I could not keep it alive in mine unfortunately, the water params in both tanks were just too much for it
. Looking back I should of acclimated it for a few days....I just did not have the time nor extra tank....it was free but lesson learned 
The guy I bought all my live rock from gave me a purple lobster, but his tank was a train wreck (covered in green hair algae). I could not keep it alive in mine unfortunately, the water params in both tanks were just too much for it