Perhaps she's a sister who was thought to be dead but actually survived. She could have been corrupted by the experiences she had while being 'dead'. When she returns, she blames Percy for not saving her properly. This false blame leads her to betray Percy. She could start spreading rumors about Percy being a coward or a bad leader among the demigod community.
One plot idea could be that Lemon has a special power that no one else in the demigod world has, and Percy has to protect her from the gods who want to use or destroy her because of it.
She might start off as a shy character. But as the fanfiction progresses and she discovers her connection to lemons, she becomes more confident. For example, if she uses lemons to make a magical item, she realizes her own capabilities and starts to stand up for herself more.
Well, a great fanfiction could be one where Percy's sister is on a quest and she finds a lemon tree in a magical grove. The lemons from this tree have special properties like they can make the person who eats them see the future for a short time. This leads to all sorts of adventures as she tries to use this newfound power to help Percy and their friends, while also keeping it a secret from those who might misuse it.
You can start by looking on fanfiction websites like Archive of Our Own (AO3). There are often many user - generated stories there. Just search for 'Percy Jackson and his sister Lemon' in the search bar, and you'll be presented with a list of relevant fics.
One common theme could be family loyalty. Since they are siblings, many fanfictions might explore how they support and protect each other. Another theme could be growing up. They may face different challenges as they get older and fanfictions can show how they deal with those changes together.
Percy would likely be very confused at first. He'd probably feel a mix of anger and sadness. He might start to question his own actions and wonder if he did something wrong to make his sister leave.
One possible plot could be Percy feeling a deep sense of betrayal and loneliness. He might struggle with his self - worth as he wonders why his sister left him. This could lead him on a journey to find answers about his family and his own identity, perhaps even uncovering secrets about his demigod heritage that his sister knew and he didn't.
The sister could be under the control of a powerful god or goddess who has a grudge against Percy. She might be forced to betray him. For instance, she could lead Percy into a trap set by the god. She could lie to him about a mission, saying it's a rescue mission but in fact it's a trap where the god is waiting to take revenge on Percy for some past deeds. This would be a really heart - breaking betrayal for Percy as he trusts his sister.
One way is through facing challenges together. For example, when they are on a quest, they might have to rely on each other's skills. Percy's sword - fighting skills and his sister's magic (if she has any) can complement each other. They also learn about each other's weaknesses and how to protect one another. In addition, they can have heart - to - heart conversations during quiet moments in their adventures, which will deepen their relationship.