Allen doesn't die. The creators of Invincible comics have kept him alive to drive the story forward and engage the readers with his ongoing adventures.
Allen in these fanfictions is typically a complex character. He has his own goals related to the Millennium Earl and the Akuma, but his feelings for Lenalee add another layer to his personality. He might be hesitant in expressing his emotions at times. Lenalee, on the other hand, is very empathetic. She is able to sense Allen's pain and tries to ease it. Their relationship in the fanfiction is usually based on mutual understanding and a growing, unspoken love that gives both of them something to fight for.
It's hard to say for sure. Some parts of the story might be based on real events, but there could also be fictional elements added for dramatic effect.