I've heard of Lionfish not eating for up to a week or a little longer after being added to a new aquarium. You might want to try something to entice them to eat. What are you attempting to feed now? Feeder ghost shrimp are a good way to get them started eating in your tank. After it starts eating, frozen meaty foods are probably the best route. Frozen silversides, krill, squid, etc are perfect for Lionfish. If it's a young fish feed 5-7 times per week, as it gets to be an adult 3-4 feedings per week is fine.
P.S. Aside from what you may hear or read it's best not to feed any saltwater fish freshwater feeders like comet goldfish, rosy red minnows, or guppies.