*This post does not deal with the medical condition; it deals with the literary condition.
The Little Mermaid Syndrome is the desire to be part of another's world.
A fictional character under the influence of LMS would go any length to become like the one they desire. This coveting is usually driven by love. In other cases the driving emotion is obsession.
The ripest situations for the LMS are in Fantasy and Paranormal genres where partners are more likely to be unmatched. By unmatched I mean a plain/weak human and a beautiful/strong supernatural being.
In these cases it is usually the human who wants become like their partner. Rarer is for the magical being to desire to be become human or have the means to become human. Plainly put it is a simple fact the LMS goes only one way.
Why is this?
I think it is all part of the escapism fantasy. We tire of the normal and are looking beyond our world for something better; be it vampires, werewolves, fairies, elves, or selkies. The idea behind this is that being connected to one of these more exotic beings or being one makes our world that much more exciting and ripe for adventure.
Human (normal) --> Vampire (supernatural)
Human (normal) --> Lycanthrope (supernatural)
Thumblina (normal, despite being supernaturally tiny) --> Fairy (supernatural)
The exception to the rule is the Little Mermaid.
Mermaid (supernatural) --> Human (normal)
This is because the human in this tale is clueless to the existence of the preternatural world. The mermaid must make herself known because their interaction would never happen otherwise as they do not exist in the same habitat. One lives on land and the other in water. It's not like with vampires or werewolves which appear completely human and can intermingle in the same locations.
Witches and wizards are to my knowledge the only magical beings that could instill the LMS in their partner and do nothing about it. You're either born with magic or you're not. There's no gray area.