Crayfish are in fact fairly herbivorous in the wild, eating decaying plant material as well as carrion. They're opportunistic though, and things like fruits, fish eggs, snails and so on will be part of their diet depending on the season. In captivity they'll eat almost anything, but supplying iodine in the form of marine aquarium iodine supplement (at half the normal dose) seems to dramatically improve their health, esp. with regard to moulting.
Cheers, Neale