In the 'harry finds a baby fanfiction', there are numerous possibilities. It could be set in a world where Harry is a grown - up and he stumbles upon a baby that is crucial to the future of his world. The story might revolve around how he deals with this newfound situation. He could enlist the help of his friends to take care of the baby. There could also be a mystery surrounding the baby's origin that Harry is determined to solve, which could lead to all sorts of adventures and revelations.
One popular one is 'A Different Destiny' where Severus finding baby Harry sets off a chain of events that deviate from the original story's path. It has great character development.
The baby could be the child of a minor character from the original series who was in hiding. For example, the baby might be the offspring of a wizard who was on the run from Voldemort's followers and unfortunately didn't make it, leaving the baby behind for Harry to find.
I'm not sure specifically as I haven't read that particular 'lucy finds a baby fanfiction'. It could be about a character named Lucy who discovers a baby in a story that is fan - created. Maybe it's in a fictional world where she stumbles upon an unexpected baby and then various adventures or emotions unfold from there.
Well, perhaps in this fanfiction, Harry Potter stumbles upon a baby while on one of his adventures. Maybe the baby has some sort of magical power that he has to protect from the dark forces. It could also be that the baby is related to an old prophecy and Harry has to figure out how to keep it safe and fulfill the prophecy at the same time.
One common plot is that Snape discovers baby Harry after the death of his parents and decides to secretly protect him. He might use his skills in potions and magic to keep Harry safe from the dark forces that are still after him. Another plot could be Snape finding Harry in a more accidental way, like during one of his forays into the Forbidden Forest. He then has to decide what to do with the baby, knowing his complex relationship with Harry's father.
In fanfiction, if Harry Potter finds a baby phoenix, it could be a very magical encounter. The baby phoenix might be in need of protection. Harry, being the hero he is, would likely take it under his wing. He could use his knowledge of magical creatures from Hogwarts to care for it. Maybe the phoenix would grow up to be a powerful ally for Harry in his future adventures.
Maybe the baby is a result of some sort of magical experiment gone wrong. And Harry Potter finds it in a hidden place where the experiment was carried out. The baby might have some strange and unpredictable magical abilities as a consequence.
It could be that the baby is from a different species or culture. Hiccup is intrigued and wants to protect it. He may have to learn new things about this baby's origin. Maybe there are some who want to harm the baby, and Hiccup has to fight against them. The story could show Hiccup's growth as a character while dealing with this unexpected discovery of the baby.
You can try searching on Tumblr. There are many fanfiction writers and fans who post and recommend stories there. Look for tags like #Snape #HarryPotter #Fanfiction #SnapeFindsBabyHarry. Some users might have their own collections or reblogs of great fics in this genre.
Sorry, I can't really recommend a specific 'harry finds a baby fanfiction' as there are so many out there and I don't have a comprehensive list of them. You could try searching on fanfiction websites like Archive of Our Own or FanFiction.net and use those keywords to find some interesting ones.