One popular storyline is where Katie has to pretend to be Logan's girlfriend for a publicity stunt. This leads to a lot of funny moments as they navigate through fake dates and public appearances. They start to develop real feelings for each other during this process.
In some fanfictions, they meet through mutual friends. For instance, one of Katie's friends is dating one of the other members of Big Time Rush, and they all end up hanging out together. That's when Katie and Logan first cross paths.
A really interesting fanfiction could be set in an alternate universe where Logan and Kendall are not part of Big Time Rush. They could be normal high school students who meet by chance. Logan is the shy nerd and Kendall is the popular jock. They initially don't get along but gradually form an unlikely friendship as they discover they have more in common than they thought.
Logan could be the type of person who only likes the official, original works and doesn't care for fan - created content. Since fanfiction is made by fans and not the original creators, he may choose to ignore it. Also, if he doesn't like the style or themes that are often explored in Big Time Rush fanfiction, he would naturally avoid it.
Katie's sickness in fanfiction can also be used as a way to show the family - like bond between her and the Big Time Rush boys. If she's sick, they might act like overprotective brothers. They'll hover around her, make sure she's warm, and tell her stories to keep her entertained while she recovers.
In the fanfiction, Logan is backstage after a particularly rough concert. The crowd was unresponsive, and he feels like he let the whole group down. He sits in a corner, his head in his hands, and silent tears stream down his face. His friends try to comfort him, but he just keeps replaying the moments of the concert in his head, feeling like a failure.
Maybe he's having relationship troubles. If the fanfiction is exploring the personal lives of the Big Time Rush members, Logan could be heartbroken over a girl. He might have fallen for someone who doesn't feel the same way, or there could be some misunderstanding between him and his love interest that's making him cry.
It could mean that Logan simply has no interest in Big Time Rush fanfiction. Maybe he doesn't like the idea of fictional stories based on the band, or he just has other things he'd rather focus on.
In some fanfictions, Logan's sister is an artist in her own right. She could be into painting or writing, and this could intersect with Logan's life in Big Time Rush. Maybe she uses her art to tell the story of Big Time Rush from an outsider's perspective, which could be really interesting. Or perhaps she gets inspired by the music and energy of Big Time Rush to create her best works, and Logan is there to support her as well, creating a symbiotic relationship between their two worlds in the fanfiction.