Loki could enlist the help of some unlikely allies. For example, he might strike a deal with a creature from the realms outside of Asgard. In exchange for a future favor, this ally helps him escape by providing a means of transportation or a way to bypass Asgard's defenses.
Another way is by disguising himself. He could change his appearance to look like a common Asgardian citizen or a visiting diplomat. Then, he could simply walk out of Asgard without raising much suspicion, using his charm and wits to get past any checkpoints.
Maybe he gets help from his friends. For example, Ron and Hermione could come up with a plan. They might send him a magical object that can help him escape, like a flying broomstick that he can use to fly away from the Dursleys' house without being noticed.
One reason could be that Loki feels constantly overshadowed by Thor. In the Asgardian hierarchy, Thor is often seen as the golden child. Loki, being the more complex and misunderstood one, might run away to find a place where he can be his own person without living in Thor's shadow.
Another possibility is that Loki teams up with other characters. He could form an alliance with the Avengers or some other powerful beings in the universe. Together, they could come up with a plan to stop Thanos. Loki could contribute his unique skills, like his ability to shapeshift and infiltrate Thanos' ranks, and then they could launch a coordinated attack.
In the fanfiction, Loki's hatred for Asgard might make him more of an anti - hero. In the original canon, he has complex relationships with Asgard, but not always pure hatred. Here, his actions are likely to be more extreme as he is driven by this strong negative emotion.
It could potentially make his relationships more complex. Some might view him with suspicion, thinking he has ulterior motives for being an Odin fan. Others might try to use this knowledge to their advantage, perhaps to manipulate Loki or gain favor with Odin.
They could use magic to disguise themselves. For example, Hermione is very skilled at the Polyjuice Potion, so they might use that to change their appearances. They would also need to be careful with their magic use to avoid detection by the Ministry's trace. Maybe they would use non - traceable magic like some ancient spells that are not well - known.
One possible reason could be his feeling of being an outcast. In the original stories, Loki is often treated differently in Asgard due to his nature. He might have felt like he didn't truly belong, which could fuel his hatred. Another reason could be envy. Maybe he saw others in Asgard having things he desired, like power or recognition, and his envy turned into hatred.
The storyline might then take different directions. For example, Hermione running away could lead her to new adventures on her own. She could discover new magical abilities or meet new characters who will help her grow. Meanwhile, Draco might have his own character development as he reflects on why Hermione left. He could either become a better person trying to win her back or turn even more bitter. Overall, it can greatly diversify the plot.
He could meet the Frost Giants. Since he has some connection to them already, they might welcome him or at least be intrigued by his presence. He could learn more about his heritage from them and maybe even form an alliance.
Well, in some fanfictions, Lucius might use his charm and power. He could be depicted as very persuasive and use his status in the wizarding world to make Hermione see him in a different light. Maybe he offers her opportunities for knowledge or power that she doesn't get with Draco.