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.
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.
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.
Arya Stark is one of the most beloved characters from 'Game of Thrones'. She is initially presented as a bit of a tomboy, not conforming to the ladylike standards of her society. As the story progresses, she becomes a key player in the power struggles of Westeros. She is brave, resourceful and has a very distinct personality that makes her stand out among the many characters in the series.
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.
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 fanfiction is 'The Sisters' Reunion'. It beautifully explores Arya and Sansa's relationship after their long separation. It shows how they learn to trust and rely on each other again, with vivid descriptions of the Westerosi setting.
There's also 'Sansa and Arya's New Adventures'. In this fanfiction, they embark on a journey across the Seven Kingdoms to discover secrets about their family. Along the way, they encounter old enemies and make new allies. It's full of action and the exploration of their sisterly bond.
One great Arya and Jon fanfiction is 'The North Remembers'. It shows a unique bond between them as they face the challenges in the North together. It has some really interesting plot twists and great character development.
I would recommend 'Jon and Arya: The Reunion'. This fanfiction is short but sweet. It focuses on the emotional moment when they finally see each other again. It doesn't get into a lot of complex plotlines but rather just gives you that warm feeling of their sibling love.