You won't find this fish in the standard fish identification books for the Caribbean: they are an invasive species. One theory is that they were aquarium fish that were released in the Caribbean. They are causing challenges because they are voracious eaters and have no natural predators outside the Pacific. In all my diving, this is the only fish that I have actively looked for to kill (I'm a "take nothing but pictures, leave nothing but bubbles" kind of diver), but the strategy is to try to slow their spread as much as we can while encouraging their predators in the Pacific (sharks, barracuda, groupers, ...) to eat them. Once the genie is out of the bottle, we can't ever eliminate them, the idea is to slow them to buy time for predators to realize they are food. Besides, lionfish ceviche is surprisingly good!
The divemasters fed any lionfish they caught to sharks and barracuda, again with the goal of teaching them to eat lionfish. They are definitely getting the hang of that: the barracuda recognize the sound of the spear elastic shooting and start hanging around waiting for the invitation. I'm not sure if they are learning that lionfish are something that they can hunt or if they are learning that divers will feed them lionfish.... On the upside, there are some fish that have been seen actively hunting the lionfish (including queen triggerfish Wikipedia).