Yes, there are some. You can find them on various fanfiction websites. Some might explore an alternate universe where Batman and Cheetah have a complex relationship, perhaps starting from an unexpected encounter and developing into something more.
Another theme is power and how it's used. Batman has his gadgets and skills, and the Cheetah has her super - speed and strength. In fanfiction, they often clash over who is more powerful or how their powers can be used against each other. For example, some stories might focus on Batman trying to outwit the Cheetah's brute strength with his intelligence. Also, there can be themes of redemption. Sometimes the Cheetah is written in a way that she might be redeemed or at least have a change of heart due to her interactions with Batman.
One idea could be a story where Batman has to face a new, more powerful version of Cheetah that has formed an alliance with some of Gotham's underworld. He has to use his detective skills to figure out her motives and weaknesses.
The relationship can be portrayed as a complex one. It could start as an adversarial relationship, with Batman trying to stop Cheetah's criminal activities. But as the story progresses, the 'lemon' aspect might suggest a more passionate connection developing between them. Maybe they start to understand each other on a deeper level, realizing that they are not so different in some ways.
The key elements could be the characterizations of Batman and Cheetah. Batman is known for his detective skills and gadgets, and Cheetah for her super - speed and feline - like abilities. In this fanfic, it might focus on how these abilities play out in their encounters. Also, the 'batman and cheetah lemon fanfic' could have elements of a power struggle. Batman is used to being in control, but Cheetah is a formidable opponent. And if the 'lemon' is about a more passionate side, it could add an interesting layer to their relationship, like a love - hate dynamic.
A common theme is the power struggle. Batman is a powerful hero and Cheetah has her own set of powers. Fanfiction often delves into how they match up against each other in terms of strength and strategy. Also, the theme of a forbidden love or attraction between them is quite popular. Despite being on opposite sides, some writers like to explore the idea of an emotional connection between the two characters. There are also stories that focus on Cheetah's origin and how Batman might interact with her during different stages of her becoming the villain she is.
One great place to find Batman and Cheetah fanfiction is on Archive of Our Own (AO3). It has a large collection with various interpretations of their relationship. Another option could be FanFiction.net, which also hosts a number of stories featuring these characters.
The theme of attraction in an unlikely pairing also exists. Despite being on opposite sides, there can be an underlying attraction between Batman and Cheetah in some fanfictions. This creates a lot of tension and drama as they struggle with their feelings while still being enemies. It's a very interesting dynamic that makes for engaging reading.
One idea could be a story where Batman has to team up with Cheetah to stop a greater evil that threatens both their worlds. Maybe a powerful alien force that is trying to take over Gotham and the jungle Cheetah hails from.
Common themes often include the struggle between good and evil within the relationship. Since Batman is a hero and Cheetah is a villain, there's a lot of room for exploring how their moral compasses interact. Also, themes of power dynamics can be present. Batman has his own set of skills and gadgets, while Cheetah has her super - speed and strength. How they balance or compete in terms of power in the relationship is often explored. Additionally, themes of secrecy and identity might be there as Batman has his double life and Cheetah also has her own secrets.