a few years ago both of the Bay Islands seem inundated with lion fish. The last couple of years, the populations were much lower. The local dive masters think that the Sharks have learned to hunt lion fish.
I spent 3 years living and working the Bay Islands. I'm not trying to discredit what you were told, but there is a horrifying lack of sharks, groupers, and snappers in the Bay Islands solely because of over fishing. If a dive center published swimming with a hammerhead on Monday at Black Hills, by Wednesday a local was showing off the shark strung up at the dock. Speaking of Utila specifically, that island only has 4 DM's worth a darn (Adam and Josh at Laguna, Bella at Deep Blue, and Bogdan on the Cayes). Everyone else ther eis just passing through on the travel circuit. The reason for the decline in population for Utila is because of the over-ambitious DMs and DMTs at the dive centers. That island pumps out DMTs perhaps second to none, and every one of them is excited about hunting lionfish. For what that is, they've done a nice job of cleaning up the recreational depths around the island. Now if they could only get the locals to stop killing everything that swims...
My landlord used to go out fishing once a week or so. Coming back with buckets of conch and cracking the shells right on their dock was no big deal. You could tell there was a sense of uneasiness around though, when I would walk down and see what they were doing. It was illegal, but nobody cared for the most part. My neighbor reported them once, she was evicted from her apartment the next day while the landlords were asked to return the now dead conch shells to the sea (but keep the meat) and issued no fine because the marine park was good friends with this family. Or the time the landlord was showing off a huge rainbow parrotfish he speared as he says to me, "I haven't seen this parrotfish here at this size since before my son was born (he was 14)." So naturally he had to spear and kill it. This was quite normal there and I don't say this to be passing judgement on them. It's how they've always lived - from the sea. And this ins't picking on Utila because it's like this in many islands across the Caribbean. Jamiaca anyone? I'm just saying until that way of thinking is changed you are not going to see the populations of the big predators rebound. Without the big predators, there is little hope because every island can't be packed with 20 year olds wanting to dive dive dive and kill kill kill lionfish. And even then they can only go down to recreational depths... without the predators rebounding those reefs are in trouble.
The flip side is the lionfish presents itself as the perfect "feeder fish" despite its tricky spines. Slow moving, plentiful... if we give the apex predators a chance it could be a quick rebound feasting on the bountiful lionfish.
Except for the green morays. revisit the thought in about 2-3 years and see how the populations look then.