These are an invasive species in the Caribbean (best guess is released from aquariums, not sneaking up the Panama Canal) and various places have different strategies. Some dive operations actively hunt them, but the group I was with just left them alone. There did not seem to be too many (I have seen invasions where the bottom just seems to crawl with the invading species...). The difficulty is that the Caribbean counterparts to the Pacific fish that prey on lionfish (groupers, sharks, barracuda) do not yet recognize them as prey, so the lionfish have few predators. People are starting to report seeing groupers hunting and eating them now, which is good news for a restored balance.