Scientists have struggled to find a way to stem the invasion of the Lion Fish, which lay as may as 30,000 eggs every four days (see here). But the answer is obvious: humans are fully capable of over-fishing the edible species to more manageable levels. Cooked to 400 degrees, the Lion Fish is rendered non-toxic and delectable (see photo below).
We just need an aggressive marketing campaign to get people to demand Lion Fish at their local eateries. That shouldn't be a problem. After all, lobster, monkfish and Chilean sea bass (a.k.a., Patagonian toothfish) all used to be considered "trash fish," fit only for serving to prisoners. The history of the seafood industry is one of over-fishing preferred species, followed by aggressive marketing of (relative) "trash" fish, which then become the new in-demand delicacies. Monkfish that used to be thrown back as an unwanted by-catch now fetch $9-13/pound at the fish monger (see here). It should be a cinch for marketers to sell the very cool-looking Lion Fish as a sustainable food source.