Maybe it could start with Blackfire secretly admiring Robin from afar. She might observe his heroic deeds and gradually develop feelings for him. Then she could start finding excuses to be around him more often.
Some smaller, more niche fanfic communities might also have what you're looking for. For example, certain Discord servers dedicated to the fandom of the characters. But to access these, you usually need to find an invite link. You can try looking for them on Reddit, in the relevant sub -reddits. There might be people sharing links to such Discord servers where you can find fanfics about Blackfire having a crush on Robin.
I'm not sure specifically about 'robin and blackfire lemon fanfiction' as it might involve adult - oriented scenarios which are not suitable for general discussion. But if you just want to read about Robin and Blackfire's interactions, you can try some mainstream fanfiction sites. Some stories might focus on their adventures together, or how they deal with each other in different situations, like facing a common enemy or working towards a shared goal.
One common theme is the clash of different cultures. Robin is from Earth and Blackfire is from another planet, so their cultural differences often play a big role. Another theme is the idea of forbidden love, as they are often on opposite sides at first. For example, Blackfire has been an antagonist in some cases.
The relationship could also develop because of a misunderstanding. Maybe Blackfire is trying to help the Teen Titans in her own way, but Robin misinterprets her actions as being sneaky. This causes a rift between them at first. But as they work through the misunderstanding, they learn more about each other. Blackfire explains her motives, and Robin realizes he was wrong. This new understanding could lead to a closer bond, with Robin seeing Blackfire in a new light and starting to develop feelings for her.
One possible storyline could be that Blackfire initially tries to use Robin for her own gain in the Teen Titans' world. Maybe she pretends to have feelings for him to get access to the Titans' secrets. But as time goes on, she actually starts to develop real feelings for Robin, which confuses her since she's not used to such genuine emotions. Robin, on the other hand, is initially suspicious of her motives but gradually sees a different side of her.
You can try looking on fanfiction websites such as Archive of Our Own (AO3) or FanFiction.net. They usually have a wide range of fanfictions including ones about Blackfire loving Robin.
There could also be themes of sacrifice. For example, Blackfire might have to sacrifice her own goals or allegiances in order to be with Robin. Or Robin might have to make difficult choices regarding his relationship with Blackfire and his duties as a hero.
To write this kind of fanfiction, start with a strong plot. Maybe a threat to the Teen Titans that forces Robin, Starfire, and Blackfire to interact closely. As for the 'lemon' aspect, it could be about exploring their unspoken desires. Starfire might have a hidden longing for Robin that she doesn't fully understand, and Blackfire could use this to her advantage. Write detailed descriptions of their emotions and the charged atmosphere between them.
One idea could be a story where Robin is caught in the middle of a rivalry between Starfire and Blackfire, and there are some 'lemon' - like tense and passionate moments. For example, Blackfire might try to win Robin over just to spite Starfire, leading to some very emotional and charged scenes.