Often, she's portrayed as a sort of mediator. In many fanfictions, she tries to reason with Lucifer, to bring him back to the side of good or at least stop his rampage. This can lead to some really emotional scenes between the two siblings. Also, there are stories where she falls in love with one of the regular characters in the Supernatural universe, like Sam or Dean. This love story then becomes intertwined with the overarching plot of good vs. evil.
Some fanfiction authors develop her by giving her a backstory that involves her being an outcast among the supernatural beings. Maybe she was shunned because of her relation to Lucifer. This then shapes her into a more empathetic character who wants to prove herself different from her twin. She might learn about human emotions and values, which further differentiates her from Lucifer, who has little regard for such things.
One common theme is family. Since Sam has a twin sister in these fanfictions, it often explores their family bond, how they support or sometimes conflict with each other. Another theme is the supernatural world. The sister usually has to navigate the same world of demons, angels, and monsters as Sam.
One popular storyline could be Lucifer being punished for his past deeds by the main characters in the 'Supernatural' universe. For example, Sam and Dean might use some powerful magic or a special weapon to confine Lucifer and make him suffer for all the chaos he has caused. They could send him to a desolate dimension where he has to endure constant pain as a form of punishment.
One common plot is that they discover their powers together. Since they are twins, they might have a special connection related to their powers that helps them in the fight against supernatural threats.
Gabriel's twin sister in the fanfiction could be a powerful force for good or evil. If she's good, she could be a key player in the fight against the demons and other dark forces. She might use her powers, which could include things like enhanced telepathy or the ability to teleport large groups of people, to help the hunters. On the other hand, if she turns out to be evil, she could be a new and formidable adversary. Maybe she was corrupted by the same forces that tried to use Gabriel, or she has her own reasons for going down a dark path. This would create a whole new dynamic in the Supernatural story.
In fanfiction, many stories revolve around Lucifer's fall from grace in more detail. Writers explore what really happened and how God felt about it. There are also stories where Lucifer becomes a sort of anti - hero, fighting against other forces of evil while still being at odds with God. Some fanfictions also play with the idea of an alternate universe where God and Lucifer have a completely different relationship, like being equal partners or Lucifer being the one in control.
A common theme is the battle between good and evil. In both Supernatural and Lucifer, this is a central concept, and fanfictions often explore it further. For example, how characters are tempted by evil or strive to do good in difficult situations.
One common trait is strength. Whether it's physical, mental, or magical strength. They need to be able to stand up to Lucifer in some way. For example, if it's an angel as his mate, they would have significant angelic powers.
Perhaps Kayla is the key to solving a major mystery in the Supernatural world. She might hold the knowledge or ability to defeat a powerful new villain that has emerged. This could lead to a series of adventures where she teams up with different characters from the show to uncover her true potential and save the day.
One possible plot could be that Gabriel's twin sister has been hidden away by their family for some reason. When she finally emerges, she has powers that are different from Gabriel's but equally as strong. She teams up with the Winchesters to fight against a new, powerful enemy that is threatening the world.