Yes, there might be such a fanfic in the fan community. Fanfics often explore different and sometimes dark or alternative storylines. Writers might create a scenario where Clementine kills Carver for various reasons, like revenge for something he has done to her or her friends in the fictional world.
One common theme is power struggle. Clementine often finds herself in situations where she has to either gain power or fight against those with more power in the Overlord universe.
I'm not entirely sure as I haven't read it specifically. But generally, a web novel might be about adventures, characters' growth, and a fictional world. It could involve things like battles, magic or some unique social systems within the story world.
One possible plot could be that Carver has kidnapped Clementine's friends and is using them as leverage. Clementine, being brave and resourceful, manages to break in to save them. In the process of rescuing her friends, she is faced with Carver and, after a tense confrontation, kills him to end his tyranny.
Well, it might be unique because it combines different fictional universes or concepts. If Clementine is from one story and the Overlord from another, the fanfic writer has the opportunity to blend their characteristics, storylines, and settings in a way that's not seen in the original works. The 'lemon' part, depending on how it's used, could introduce a new level of emotional and physical intensity to the relationships within the fanfic, which is quite distinct.
The unique combination of characters. If the fanfic can explore the relationship between Clementine and the Overlord in an unexpected way, it can be really interesting.
One great 'Clementine Overlord' fanfic could be 'Clementine's Ascent in the Overlord World'. It has an interesting plot where Clementine uses her wits to survive in the Overlord universe. The character development is quite engaging as she adapts to the new and often dangerous environment.