Arya could use a lemon as a secret signal related to her family. Catelyn taught her this long ago. So when Arya is in a dangerous situation, she leaves a lemon as a sign that she is from House Stark. This way, it becomes a connection between her and her mother's teachings.
In a fanfiction, the lemon could be a gift from Catelyn to Arya before all the chaos in Westeros began. Arya has carried this lemon or something made from it, like a lemon - scented handkerchief. Whenever she feels lost or in need of her mother's strength, she takes it out. It serves as a physical and emotional link between them.
Maybe in the fanfiction, there is a prophecy that involves Arya, Catelyn and a lemon. For example, it could be foretold that a Stark daughter (Arya) will use a lemon to find a path that was once shown to Catelyn in a vision. Arya then embarks on a journey to discover the meaning of this prophecy and in the process, she uncovers more about her mother's past and her own destiny.
One idea could be that Arya, while on her travels, comes across a lemon tree in a strange land. She remembers her mother Catelyn's love for the smell of fresh things. So, she decides to take some lemons with her to bring a bit of home. When she finally returns to a place where she can reunite with Catelyn's memory, perhaps through an old family friend, she uses the lemons to make a special drink or offering in her mother's honor.
In the fanfiction, Arya might see the lemon as an opportunity. Since she's always been resourceful, she could think of ways to use it to her advantage, perhaps in her battles or quests. Catelyn would be more concerned about the implications of this strange object in their world. Harry Potter, with his knowledge of magic, could try to communicate with the lemon if it had some sort of magical essence. He might also try to protect Catelyn and Arya from any potential harm the lemon could cause, while Arya might be more eager to take risks with it.
One idea could be a story where Arya meets Lemon in a tavern during her travels. Maybe Lemon has some interesting information about Arya's enemies, and they form an unlikely alliance to take on a common foe.
Perhaps the lemon is a key element in a prophecy. In this fanfiction, Catelyn has a vision that involves a lemon, Arya, and elements from the Harry Potter universe such as Hogwarts. Arya is on a quest to find out more about this prophecy. She teams up with characters from both worlds, and together they try to decipher the meaning of the lemon in the prophecy. It could be that the lemon represents a source of power that can either save or destroy their world, much like the Horcruxes in Harry Potter.
Arya and Tywin could also interact in a more unexpected way. Maybe in a situation where they are forced to work together for a short time due to some external threat. During this time, Arya has to constantly remind herself of her ultimate goal of revenge while Tywin is constantly on guard against her, yet also seeing potential in her skills for his own purposes.
One great 'Game of Thrones Arya Stark' fanfiction is 'Arya's New Path'. It focuses on Arya's journey after leaving the Faceless Men, exploring her newfound skills and how she uses them to help the common people. It has a lot of character development and great descriptions of the world.
A simple plot could be that Arya and Lemon cross paths in a forest. They both have different goals but realize they can achieve more together. So they team up to hunt down a group of outlaws who have been terrorizing the local villages.
The relationship could develop into a strange sort of mutual respect. Maybe Arya saves Tywin's life in a situation, and Tywin, in return, offers her protection. They start to understand each other's motives more deeply. Arya realizes that Tywin is not just a heartless monster but a man with his own goals and Tywin sees Arya as a force to be reckoned with rather than just a Stark girl to be eliminated.
Often in Arya - Game of Thrones fanfiction, she is presented as a force to be reckoned with. Writers may put her in situations where she has to use her wits and combat skills to overcome great challenges. She could be in a scenario where she has to infiltrate an enemy stronghold all by herself, relying on her training from the Faceless Men and her own natural instincts as a Stark.
Sansa in fanfiction is often painted as a more refined character. She's the one who might be seen attending grand balls and making strategic alliances through her conversations. Her development in fanfiction usually revolves around her political acumen. Arya, however, is shown as a more free - spirited and vengeful figure. She's not afraid to get her hands dirty. Fanfiction might show her prowling the streets at night, using her skills to right the wrongs. These different portrayals not only reflect their original character traits but also allow fanfic writers to explore different storylines for each of them.