The first thing is, how long have you had the lionfish? If you have had him for awhile and he has learned to associate you with food, then skip the next bit. If you have had him only a short time, then you need to teach him that you are the source of all things edible! To do this you start feeding him live ghost shrimp. Give him a couple of shrimp, every few days. Once the lionfish comes to the front of the tank, and waits for you to put the shrimp in, you will know you are ready to switch him over.
Stop all feedings for a week. Then offer him a live ghost shrimp followed immediately (as soon as the lion has caught the shrimp and has returned to the surface) with a piece of thawed food. Use a silver spoon to feed him the dead food as the flash of silver will help to stimulate him to strike. Then give him another ghost shrimp. Stop all feedings for 5 days. Repeat the feeding above, only this time, skip the last shrimp and give thawed food instead. After that he should be eating anything that hits the water!
Remember not to overfeed (these guys will eat till they burst!) and don't feed every day. Every two to three days is better for them. Offer them a variety of foods like shrimp, squid, clams, silversides.
Good luck!