First, know the characters well. Study their personalities, backstories, and relationships in the original Birds of Prey material. Then, come up with an interesting plot that can incorporate the romantic or 'lemon' elements in a natural way. For example, you could create a situation where two characters are forced to work together closely and feelings start to develop. Also, use vivid descriptions to bring the world of Birds of Prey to life in your fanfic.
In a crossover with the Inhumans, Medusa could be one of the main characters along with the Birds of Prey. Her long, prehensile hair and leadership skills would create an interesting dynamic. Also, in a crossover with the Guardians of the Galaxy, Gamora could be a main character. Her combat skills and no - nonsense attitude would mesh well with the Birds of Prey.
One idea could be to have the Birds of Prey cross over with the X - Men. Maybe the Birds of Prey are on a mission in a mutant - heavy area and have to team up with some of the X - Men to take down a common enemy. Another idea is a crossover with the Justice League Dark. They could combine their skills in magic and combat to face a supernatural threat that neither group could handle alone.
One common trope is the 'enemies to lovers' where the characters start off on opposite sides or with some sort of conflict and then develop a romantic relationship. For example, in the 'birds of prey' universe, two characters who are initially rivals in the criminal underworld might fall in love.
You can try looking on some popular fanfic websites like Archive of Our Own (AO3). It has a large collection of various fanfics, and there's a good chance you'll find 'birds of prey lesbian fanfic' there.
The story of the peregrine falcon is also great. Peregrine falcons were once endangered due to pesticides. But through conservation efforts, their population has rebounded. There was a peregrine falcon pair that nested on a skyscraper in a big city. People watched in awe as they raised their chicks, adapting to the urban environment while still being magnificent hunters.