Not to be technical, but I don't believe there is a such thing as a FW lobster. They are all crayfish (or crawfish/crawdad whatever you prefer).
As for putting crayfish into a tank with fish.... really a bad idea if you like your tank. They might be fine now, in a month, or in a year but they will turn on your fish. As for them catching fish, they are quite adept at it... there is a thread that's not too old of someone's crayfish that won't eat dead fish because it likes the live ones more.
I think a better idea would be to find a shrimp (there are plenty of larger ones) that won't eat fish (plenty of them).