Do you want fresh-water or salt-water? I know there are fresh water crabs but I'm not sure about lobsters.
one of my friends had a crab in his tank once, it was great to watch and appeared rather peacefull ... until one night, (previously we had noticed fish disappearing, even larger ones so we had no idea where they had gone (we all know where this story is going dont we?!) I was watching his tank, when suddenly, the calm, still crabbed lashed out at a passing by fish, cought him in his claw and began chomping at him, bit by bit. At this disterbing site, the crab was returned the next day.