Yes, there are some out there. You can start by looking on fanfic websites like Archive of Our Own. However, the quality can vary greatly. Some might focus more on character development in this new relationship context, while others might be more plot - driven.
Archive of Our Own is a great place to start. It has a large collection of fanfic from various fandoms, including 'Game of Thrones'. Just use the search function and type in relevant keywords like 'Catelyn Stark' and 'lesbian' to find what you're looking for.
Catelyn Stark is interesting for fanfiction because of her complex personality. She is a strong - willed woman in a male - dominated world. Her loyalty to her family is unwavering, yet she also has to make tough decisions that sometimes put her at odds with others. This creates a lot of potential for different storylines in fanfiction.
One type of fanfiction could be about Catelyn Stark's backstory that wasn't fully explored in the original series. It could show her growing up, her early days of marriage, and how she developed her strong will. Maybe it delves into her relationship with her family members before the events of the main story, like her parents and siblings, and how that influenced the person she became in Game of Thrones.
In many Catelyn Stark time travel fanfictions, it can completely change the plot. For example, if she travels back and stops Ned from going to King's Landing, it would prevent a whole chain of tragic events. This is because Ned's presence in King's Landing was a catalyst for many power struggles and betrayals.
One great fanfic could be about Arya Stark rebuilding Winterfell as the last Stark. It might explore how she uses her skills she learned during her travels to bring back the glory of her family's home. She could train new guards, establish trade routes, and make Winterfell a stronghold again.
In some fanfics, Arya Stark might be presented as the last Stark, but it really depends on the specific plot and direction the fanfic author takes. There could be plot twists where other Starks are revealed to still be alive.
It could be a bastard child of a Stark that was kept hidden for some reason. Maybe for fear of political ramifications or because of some dark family secret.
Another idea for a fanfic is that Arya discovers she's not really the last Stark. There could be a long - lost relative hidden away. She then embarks on a journey to find this person. Along the way, she has to overcome many obstacles and face new enemies, all while trying to keep the hope of the Stark family alive.