I have two Lionfish, one an antennatae and the other a Russells. The Russells is pretty small (head to tail about three inches) and the antennatae is around 6 inches.
Neither one would eat (though I am mysteriously missing two cleaner shrimp and three chromis) for about two weeks and the antennatae still will not take any offerings.
The Russells eats anything, even Shrimp and scallop pieces. If you have trouble feeding, get some frozen krill or shrimp from YLFS and drop it into a jet stream or water return. If you have thawed out the shrimp, when it hits the jet, it will move quite quickly and life like. If the Lion is close by, the rapid movement will stimulate him.
Someone explained to me that since they are predators, they size up prey by it's eyes, they attack and move when they feel they aren't being watched. I don't know if that's true, but the Russells didn't eat anything until I offered shrimp (with tiny black eyes), and now he'll eat anything.
Don't overfeed, these bad boys will stuff themselves. They also seem to be among the more intelligent fish with a great personality. The Russells will come to the edge of the tank when you enter the room and follow you as you walk by.
Hope this helps. Stay patient, these guys don't need to eat everyday; 2-4 times a week should be more than fine.