Gut-packed ghost shrimp, mollies, and guppies are good to get them started. Once they are acclimated there's really no reason (most of the time anyway) that they can't or won't eat frozen food. Krill, mysis, silversides, shrimp, scallop, clam, squid, fish flesh, (you get the idea) and more. Variety is important, for health and colour. I work at an LFS and I won't sell any lionfish that isn't eating frozen food (this is because where I am, people have this obsession of feeding ANY of their fish with goldfish, it's beyond me). IME, most of the time when a lionfish won't take frozen food, it's because the owner is afraid that it'll starve to death and if it doesn't eat prepared food right away they continue live food.
I'm not saying live food can't be used (just make sure to gut-load), its just more expensive and less convenient.