First, you need to understand the original characters well. Know their personalities, motives, and relationships. For example, the students' different assassination skills and how they interact.
One great 'assassin classroom fanfiction' story is the one where the students go on an unexpected adventure outside of the classroom setting. It really explores their characters in a new light.
DeviantArt can also be a source. Sometimes, artists not only post their art but also write short fanfiction pieces related to Assassin Classroom. It might not have as extensive a collection as AO3, but the ones you find there can be really unique. They might combine art and story in an interesting way. Additionally, Reddit has some subreddits dedicated to Assassin Classroom where fans might share their favorite fanfictions or even their own works.
A great aspect is that it allows you to keep the story alive in your mind even after the anime or manga has ended. You can find fanfictions that continue the story from where it left off. Some might explore what happens to the students after they graduate. Also, reading fanfiction can introduce you to a community of fans who share similar interests. You can discuss your favorite fanfics and even get recommendations from others.
Another theme could be her own growth as a character. In the series, she has her own journey, and in fanfics, this can be expanded upon. For instance, she might have to deal with personal issues outside of her teaching role, like her past relationships or her family. And how she overcomes these things can be a major part of the fanfic. It gives the author a chance to delve deeper into her character than what was shown in the original series. This can make for some really engaging stories as readers get to see a different side of her.
There are probably some on Archive of Our Own as well. The great thing about AO3 is that it has a wide range of fanfics with different themes. In the case of Karasuma Irina fanfics, you might find some that are more centered around her character development, like how she becomes a better teacher or how she overcomes her own insecurities in the 'assassin classroom' world.
One possible fanfiction could be about Nagisa, as a girl, having to deal with the unique challenges in the Assassination Classroom. Maybe she uses her newfound femininity to her advantage in different assassination attempts. For example, she could play on the stereotypes that others might have of a girl being less of a threat, only to surprise her opponents.
One possible fanfiction could be about female Karma's journey in the Assassination Classroom. Maybe she uses her intelligence and unique skills to outwit the other students in various assassination attempts. For example, she could come up with creative plans to get close to Koro - sensei while still maintaining her cool and mysterious demeanor.
I'm not entirely sure specifically as 'lemon' in fanfiction often implies some romantic or slightly more mature undertones, but in general, a Naruto classroom fanfiction might be about Naruto characters in a classroom setting. It could involve their daily school lives, relationships among classmates, and how they learn ninja skills in an academic-like environment.
One characteristic is the exploration of the unique characters. Fanfictions often dig deeper into the backstories and personalities of the students and the teacher in 'Assassination Classroom'. For example, they might expand on how Nagisa came to be so calm and observant. Another aspect is the different plot twists. Some fanfictions create alternate scenarios where the assassination attempts take on new forms or have different outcomes.