Dumbledore could play a role too. He has vast knowledge and connections. He might give Harry some hints or direct him to certain places or people who can assist in finding the cure for lycanthropy.
One possible plot could be that Harry, with the help of Hermione's research, stumbles upon a long - forgotten alchemical formula. They then search for the ingredients all over the wizarding world. Harry faces many challenges, like dealing with dark wizards who want to stop him from finding the cure because they want to use werewolves for their evil plans. But in the end, he manages to make the cure and uses it on Lupin, who then becomes a normal wizard again.
His best friends Hermione and Ron would surely be there to help. Hermione with her vast knowledge of magic could research about the egg, and Ron with his loyalty would stand by Harry's side in any danger related to the egg.
Yes, there are likely many fanfics out there about a lycanthropy cure in the Harry Potter universe. You can try searching on fanfic platforms like Fanfiction.net or Archive of Our Own.
Hagrid would be a likely helper. He has a great knowledge of magical creatures and would surely know a lot about phoenix eggs. He could give Harry advice on how to take care of it.
Dumbledore could also be involved. He's extremely knowledgeable and powerful. He might have some secret knowledge about basilisk eggs. He could guide Harry on whether to keep the egg or destroy it, depending on the greater good of the wizarding world.
Hermione would most likely help. She's always been there for Harry, and with her vast knowledge from books, she could offer a great deal of advice on how to take care of the dragon egg. Ron might also be involved. Despite his initial fear of things, he has a brave heart and would probably stand by Harry's side.
One idea could be a potion made from rare magical plants found only in the Forbidden Forest. Another might be a spell that requires the combined magic of a werewolf and a powerful wizard. Or perhaps a magical artifact that has the power to reverse the lycanthropy curse.
Neville could be another helper. He has become quite skilled in herbology. He could help Harry by creating a magical garden around the house. The plants in the garden could be used for protection, like thorny bushes that keep unwanted visitors away, or for providing ingredients for household potions.
Dumbledore might help from beyond the grave, in a sense. Harry could discover some of Dumbledore's old notes or memories that provide crucial insights into building a powerful and controlled bomb. And perhaps some of the more eccentric professors at Hogwarts, like Professor Flitwick, could offer their expertise in charms which might be needed for the bomb's construction.
There could be a group of magical creatures who see the snake as an abomination or a threat to their kind. They would try to destroy the snake and Harry would have to protect it. These creatures could be from a part of the Forbidden Forest that has not been explored much in the original books and they have their own set of rules and magic which makes them a formidable antagonist.