One idea could be Sonic's speed causing chaos among the Justice League at first. For example, he might accidentally disrupt Batman's plans during a Gotham operation. Another could be Sonic teaming up with The Flash to outrun a common enemy that is threatening both their worlds. Maybe they have a friendly race while also trying to lead the bad guy into a trap.
Perhaps in the fanfiction, Sonic is transported to the Justice League's universe and is mistaken for a meta - human. The League tries to recruit him, but Sonic is more interested in finding a way back home. However, as he gets to know the members of the League and the threats they face, he decides to help them out for a while. This could lead to Sonic using his unique abilities to help the League in battles against villains like Darkseid or Lex Luthor, and in the process, he forms new friendships and learns about different ways of fighting for justice.
One idea could be that Robin is on a solo mission when he accidentally stumbles into a Justice League operation. He then has to prove himself to the League members and ends up joining them for that particular mission. Another could be Robin discovers a secret about a member of the Justice League that puts him in a difficult position of whether to expose it or not.
One idea could be that the Flash from Arrowverse accidentally runs into a different dimension where he meets the Justice League. He then has to team up with them to stop a powerful villain that is threatening both his world and the Justice League's world.
A possible plot could involve a member of the Batfamily getting kidnapped and the Justice League helping to rescue them. During the rescue, they discover a secret weapon or technology that the villains were planning to use against the world, and they have to work together to stop it.
A possible plot for 'sonic meets sonic boom fanfiction' is that a strange rift in the dimensions brings Sonic and his friends from the classic Sonic world into the Sonic Boom world right when they are about to have a big celebration. However, the Sonic Boom characters are initially suspicious of these new arrivals. But as they start to realize that a common enemy is behind the rift, they join forces. Sonic and Sonic Boom Sonic could have a friendly competition to see who can defeat the most badniks during the adventure, which also helps them bond and understand each other's strengths better.
One idea could be a crossover where the Young Justice team has to team up with the Justice League to face an interdimensional threat. Maybe a powerful villain from another dimension is trying to invade Earth and the combined skills and powers of both groups are needed to stop it.
Maybe a story where some of the younger members of the Young Justice team are frustrated with the Justice League's methods and decide to take on a mission on their own, but end up getting in over their heads and have to call in the League for help. This could lead to a lot of character development and some interesting dynamics between the two groups.
One idea could be that Sonic from Sonic X accidentally travels to the Sonic Boom universe and has to adapt to the different environment and new versions of his friends. Maybe he teams up with Sonic Boom Sonic to defeat a common enemy that has found a way to cross between the two universes.
One idea could be that the Justice League members gain new gaming - related powers. For example, Superman could have the ability to instantly analyze any opponent's weaknesses like a game character stats screen. Batman could use his detective skills to hack into virtual reality systems within the story's universe.
One idea could be a story where Batman has to lead the Justice League in a fight against a new, powerful and mysterious villain that can manipulate time. Another could be a fanfiction exploring the relationships within the Justice League when they are stranded on an uninhabited planet and have to rely on each other more than ever.
Perhaps in the fanfiction, there is a parallel universe where the Justice League are all vampires. They are trying to protect both the vampire and human populations from a greater evil that threatens to destroy both. They face challenges in getting the human - dominated Justice League in our universe to trust them and work together.