From a marine biologists pov, there are two general types of lionfish in this situation. The common lionfish and the shu man du lionfish. I get them mixed up, but one is non-invasive and the other is, and after a hurricane in Florida, myth spread that lots of captive lionfish were released because an aquarium collapsed (bare with me, this is an old story). Whochever one was in that awuarium became invasive as it engulfed the population of the other. I am pretty sure the Shu Man Du lionfish is invasive, because the aquarium my university is linked with has multiple living specemins.
(first image is Shu Man Du lionfish, second image is Common/Red lionfsih)