Well, consider the fact that the Olympians are used to being in control. In the fanfiction, the characters might act in ways that are completely against what the Olympians expect. For example, if a character defies Zeus in a very disrespectful way. Zeus would be enraged and might want to punish the character in the fanfiction world. Athena, though, might see the potential in such a character. She could think that the character's defiance shows intelligence and courage, and she might be interested in seeing how the story unfolds further with this 'rebellious' character.
Some of them might be offended. If the fanfiction portrays them in a way that goes against their self - perceived grandeur or if it misrepresents their myths and legends. For example, if a fanfiction makes Zeus look like a bumbling fool instead of the powerful king of the gods, he might not be too happy about it. However, others might see it as a form of flattery that mortals are so interested in their tales that they create their own versions.
The Olympians might find the fanfiction hilarious. Athena, being the goddess of wisdom, could appreciate the clever plot twists that fans come up with. She might even be inspired to create her own story based on the fanfiction, but in a more 'divine' way. Poseidon might be amused to see how his son Percy is portrayed in different and unexpected situations in the fanfiction.
If the fanfiction contains positive and respectful portrayals of the Olympians, they might think more highly of mortals' respect for the divine. However, if it's full of disrespect or inaccurate information, they could view mortals as being ignorant or impertinent. For example, if a fanfiction twists the facts about their powers or relationships in a negative way, it could lead to a negative perception of mortals.
The Avengers' reactions would vary widely. Tony Stark, being the tech - savvy and quick - witted one, would probably be making jokes left and right about the fanfiction. He might say things like 'Why do they need a sword when they could have a laser - sword?' Captain America, on the other hand, would be more respectful. He'd try to understand the cultural and mythological aspects of the story. Hawkeye would probably be a bit indifferent at first, but as the story goes on, he might get more interested in the action parts of the fanfiction.
Some gods might be entertained. For instance, Hermes, being the trickster god, might enjoy seeing the different and often humorous takes on the gods in the fanfiction.
Poseidon could be quite entertained by the fanfiction about his son Percy. He might appreciate the creativity of the fans. Zeus, as a rather strict and proud god, may be offended if the fanfiction doesn't uphold his dignity. Hades, who is often seen as a bit of an outcast among the gods, might be more open - minded. He could be interested in how mortals imagine his domain and his role in the story. He might also find some of the unique interpretations of his character refreshing, unlike Zeus who is more likely to be affronted by any deviation from the 'proper' view of him.
Poseidon's reaction when reading the Lightning Thief fanfiction could be complex. He may start to think about his actions in the original story differently. If the fanfiction offers new perspectives on his motives or his interactions with other characters, he could gain a new understanding of himself. He might also be a bit critical, as he has his own view of how things should be and the fanfiction may deviate from that.
I'm a big fan of Percy in fanfictions. He's always so brave and resourceful. In many fanfictions, he gets to show even more of his humorous side, which makes him really likable.
Another aspect that makes a good 'The Lightning Thief' fanfiction is the exploration of relationships. This could be the friendship between Percy and his friends, or a new romantic relationship. Fanfictions that delve deeper into how the characters interact with each other on an emotional level can be really captivating. Also, a good fanfiction might introduce new mythological elements that blend well with the existing Percy Jackson universe, like a new type of monster or a different take on an old god.