Most fanfiction platforms have strict rules against explicit or inappropriate content like lemon fanfiction. It's better to focus on non - sexual interpretations of the relationship between fem Harry and Buckbeak. For example, you could explore stories where they form a strong bond of friendship and adventure, which are more in line with the spirit of the original Harry Potter series.
One plot idea could be that fem Harry discovers she has a unique telepathic connection with Buckbeak. This allows her to understand his thoughts and feelings more deeply, and they use this connection to communicate secretly during dangerous situations at Hogwarts. For example, when there are Death Eaters lurking around, Buckbeak can warn fem Harry through their mental link.
The main characters are clearly Harry Potter and Buckbeak. Harry is the famous wizard boy from Hogwarts, and Buckbeak is the hippogriff that Harry befriends in the series.
Well, in some 'harry and buckbeak lemon fanfiction', there could be a plot where Harry has to train Buckbeak for a special magical competition. During this training, they form an even deeper bond. And perhaps Buckbeak helps Harry overcome his fear of a certain spell or magical situation by being there for him. It's all about their unique relationship and how it develops in these fictional scenarios.
At first, it might be a bit tentative. Harry has to earn Buckbeak's trust, just like in the original story. But as time goes on, they start to understand each other better. Buckbeak realizes Harry is different from other humans who might harm him, and Harry sees Buckbeak as more than just a magical creature.
Another place could be Fanfiction.net. However, the tagging system there might not be as precise as on AO3. But it's still worth a shot. Look for the relevant character names in the search bar and browse through the results. Some fanfic authors also post about their works on social media platforms like Tumblr or Twitter, so you could search there too. Maybe search for '#fem Harry #Moony #fanfiction' on Twitter for example.
As lemon fanfiction involves inappropriate content, I can't discuss its characteristics in the context of that. But generally in regular fanfiction about Harry and fem Draco, a characteristic could be the exploration of their personalities in new ways. For example, how a female Draco might have different interactions with Harry compared to the male Draco in the original story.
Another issue is that it can be considered unethical. These types of fanfiction can make some readers uncomfortable, especially those who prefer to stay true to the original spirit of the story. It also may not be suitable for younger audiences who are fans of the Harry Potter series.