Well, lemon fanfiction often involves romantic or sexual elements that are not part of the main show. In the case of Rick and Carl, it might add an inappropriate layer of relationship that goes beyond the normal father - son or comrades - in - arms dynamic shown in 'The Walking Dead'. It can also sometimes distort the characters' personalities to fit the more adult - themed scenarios.
I'm not really into lemon fanfiction as it often goes against the original spirit of the show in some ways. But you could try looking on fanfiction.net. They have a large collection of 'The Walking Dead' fanfictions, and you might be able to find some Rick and Carl - related ones there, though you'll have to filter through to avoid the inappropriate stuff.
Unfortunately, Carl did die in The Walking Dead comics. It was a sad moment for fans. His death had a big impact on the storyline and the other characters.