The answer is Lionfish are native to the tropical Pacific. There are no natural water routes of warm water between the Pacific and Atlantic oceans.
Invasive species is a species that colonizes an environment in which it is not a native species and tends to upset the natural balance of that environment. Lionfish are naturally found in the indo-pacific, which is their native environment. However, their presence in the eastern United States has have threatened the ecosystem of the region. The fish has decimated fisheries and reef ecosystem since they also don’t have natural predators in the region. Therefore, their population explodes unchecked.