Yes, there might be. The 'The Owl House' has a large and creative fan base, and fanfiction often explores various 'what - if' scenarios. However, the content can vary greatly in quality and adherence to the spirit of the original show.
Fanfiction.net could also be a place to search. There are likely some stories there that might feature this scenario. Additionally, you could try searching on Tumblr. Sometimes fans share links to their favorite fanfictions there, and you might find one about Luz being pregnant through Tumblr's search function.
One popular theme is friendship. Amity and Luz's relationship grows from a somewhat rocky start to a really strong friendship. Another theme is self - discovery. As they face various challenges in the Boiling Isles, they both learn more about themselves. Magic is also a big theme, as they use magic in their adventures together.
Well, it's hard to say who the 'best' are, but some authors have really stood out. There's this one author who goes by the name 'MagicWriter123'. Their stories often have really detailed descriptions of Amity and Luz's relationship. Another good one is 'BoilingIslesFan'. They seem to have a great understanding of the show's lore and incorporate it well into their fanfics.
If Luz was Eda's daughter, her relationship with King would be more like that of siblings. King might be a bit more protective of Luz or jealous when she gets more attention from Eda at times. And Luz would probably be more bossy towards King in a sisterly way.
Another storyline might be that Luz has to deal with the expectations that come with being Eda's daughter. Since Eda is a well - known and powerful witch, people in the Boiling Isles might have high hopes for Luz. This could cause Luz to feel pressured, but with Eda's support and guidance, she learns to be her own person and make her own mark in the magical world.
The 'the old owl witch story' could be about an old witch who is accompanied by an owl. Maybe the owl is her familiar, which is like a magical pet or helper in some witchcraft beliefs. The story could involve the witch using the owl's special abilities, like its night vision or silent flight, to carry out her mysterious deeds, such as gathering ingredients for her spells under the cover of night.
It's mainly about the adventures in a magical world. There are unique characters, like witches and demons. It shows their relationships and the challenges they face in this strange place.