Perhaps it was a memory vial. Snape had many complex memories, and he might have wanted Harry to give a particular memory to Lucius. This memory could be something that would change Lucius's view of Snape or even some important information about the wizarding world's history that Snape thought Lucius should know.
Most likely not. Popular fanfictions in the Harry Potter universe tend to focus on more relatable themes like relationships, adventures, or character backstories. This 'snot' - related concept is so far from the norm that it would probably only appeal to a very niche group, if any at all.
Well, without actually reading this specific fanfiction, it's hard to say precisely. But it could potentially be a humorous or dark exploration of the Harry Potter universe. Maybe it's a satirical piece that uses the idea of Snape's snot as a symbol of something, perhaps his disdain for Harry or some other complex emotion in a really warped way.
One possible plotline could be that Snape, in his secret attempts to rescue Harry, starts to see a different side of him. Maybe during a dangerous situation in the Forbidden Forest, Snape saves Harry from a dark creature. As they spend time together afterwards, they begin to understand each other's pain and pasts, and slowly romantic feelings start to develop.
Well, it could be that in this fanfiction, Snape is written in a way that endangers Harry's friends. Harry is very protective of his friends, so if Snape is portrayed as harming them in some way, Harry would likely try to destroy whatever it is that's causing the threat. Also, it could be related to some prophecy or hidden knowledge in the fanfiction that makes Harry believe Snape has to be stopped.
One consequence could be that he gains an unexpected ally in Draco. Draco might feel indebted to Harry and start to change his views towards him, which could lead to some interesting interactions between them in the future. This could also cause some tension among their respective groups of friends.
Hermione could be a great addition. She could be the voice of reason when Harry starts getting closer to Lucius. Her intelligence and knowledge of magic could also help in any situation they face together. Another good character would be Draco. Since Lucius is his father, it would add an interesting dynamic. Draco could be conflicted about his father's new relationship with Harry. And of course, Dumbledore. His wisdom and guidance could play a crucial role in how the relationship between Harry and Lucius develops.
Harry would probably be extremely cautious. He has a strong sense of right and wrong, and Lucius has been on the wrong side in his eyes. Harry would be analyzing Lucius' every move, trying to understand if this is some sort of new Dark Arts plot or if there's something else going on. He would also be worried about the implications for his friends and the wizarding world in general.
Harry might start as a reluctant follower of Voldemort in the fanfiction. As time goes on, he could either become more hardened by the dark environment or find a way to subvert it from within. Lucius, who was already a Death Eater, may develop a more complex relationship with Harry. He could initially see Harry as a threat to his status with Voldemort but later come to respect Harry's strength and cunning.
One great 'Harry and Lucius Fanfiction' is 'The Unlikely Alliance'. It shows an interesting dynamic where they are forced to work together against a common enemy. The author does a great job of exploring their complex relationship.