Natural Predators are a big no-no. You dont want the problem Australia had, they would just be a bigger predator that eats everything else/anything thats easy to eat.
However big Grouper eat them, but they dont really hang where the giant grouper are because they are a bit deep.
Cornet fish, certain species of large groupers and morays prey on lionfish in the Pacific.
Gray triggerfish eat lionfish flesh and maybe juvenile lionfish in the Bahamas and Florida
The large grouper is the best candiate for control in the Caribbean and Bahamas. However, the native species are way overfished and do not yet recognize the the lionfish as a prey item.
You're right. Introducing an exotic species, like the cornet fish, that "knows" how to prey on lionfish is risky.
Maybe a grouper from the Pacific is safer because it has competition from native groupers. However, it would likely be fruitless because the shallow waters in the Bahamas are so heavily fished the species would not have chance to develop anyway.
Lionfish meat is tasty and the perhaps a fishery will help to some extent.
The ideal scenario would be if certain predators like large eels, groupers and even sharks evolve a taste for lionfish.
Something has to happen because the situation is getting out of hand threatening many native species.