Caribbean Reefie hunting Lionfish - source.
Well, turns out that it aint quite good enough.
The latest research indicates that local predator size and abundance does nothing to stem the spread of invasive Lionfishes in the Atlantic, this because those local predators cant out-compete them and also, because they either simply don't perceive and/or prefer them as prey or because the success and abundance of Lionfishes is not primarily determined by predation in the first place.
And my prediction?
It was totally speculative to start with, and this latest research appears to completely negate it - and it would be foolish to invoke predator/prey cycles and wait for a total collapse of their prey, or to hope for some Lionfish-specific epidemic or the like.
So keep hunting and eating them!
It won't eradicate the Lionfishes - but if done consistently, it will at least keep down their numbers and mitigate their impact.
More about this, and invasive species in general here.