Let's look at the sentence: The long, thin fins on lionfish back and belly have stingy spines.
To make it grammatically correct, we need to add a word before 'back' and 'belly' to show whose back and belly we mean. Since we are talking about the lionfish, it should be lionfish's, which means the back and belly of the lionfish.
So, the corrected sentence is: The long, thin fins on the lionfish's back and belly have stingy spines.
This means the lionfish has long, thin fins on its back and belly, and these fins have spines that can sting.