They could be used as a form of transportation in a very unique way. Instead of broomsticks or thestrals, a wizard could enchant a swarm of butterflies to carry them. It would be a slow and more aesthetically pleasing form of travel, suitable for short distances or for a more whimsical character who wants to make a grand entrance.
They could be used to create a mystery. Say a set of bank statements has some encrypted or missing information. Harry and Hermione would use their knowledge of magic and codes to try and decipher it, leading them to a secret vault or a hidden treasure.
A black dog in Harry Potter fanfiction can be incorporated creatively by making it a part of a character's backstory. Maybe the character was saved by a black dog when they were a child in a magical accident. So, the dog becomes a significant part of their life. Also, it could be a transformed form of a cursed object. Every time someone touches the object, the black dog appears and causes chaos or reveals hidden truths.
You can make Ash a central character with unique control abilities. For example, Ash can control the movement of ash particles to create illusions or barriers. This would add an interesting dynamic to the story.
A creative combination could be that the Central Perk coffee shop is secretly a wizarding hangout in the Muggle world. The Friends gang unknowingly serves magical drinks to wizards and witches in disguise. There could be a plot where the regulars at Central Perk start to notice strange things happening, like people disappearing into thin air or cups refilling themselves. And the Friends characters have to figure out what's going on with their new 'weird' customers.
It could be a storage for ancient and dark artifacts. A group of dark wizards are after these artifacts stored in the cupboard, and Harry has to protect it. This could lead to an epic battle between Harry and the dark wizards right in his old home in Privet Drive.
One way to combine them creatively is by having an Avatar character attend Hogwarts. Imagine an Airbender learning magic, using their airbending skills to enhance their spell - casting, like using air currents to direct a spell more accurately. Another idea could be a crossover where the Avatar world's spirits interact with the magical creatures in the Harry Potter universe. For example, a Patronus could be seen as a form of spirit energy, and perhaps there could be some kind of connection or interaction between them.
One way to incorporate them could be in an adventure story. Lara could be on a quest, and the dog could be her loyal companion. The lemon could be a strange object she finds that has magical properties. For example, when the dog sniffs the lemon, it reveals a hidden path.
One way is through the wizarding economy. For example, the Weasley twins' joke shop, Weasleys' Wizard Wheezes. Fanfiction could expand on the business side of it, like how they manage inventory. They might have to source ingredients for their magical pranks from different wizarding markets. Another aspect could be marketing. How do they promote their products? They could use magical means like enchanted flyers that follow potential customers. Also, they need to deal with competition, perhaps from other prank - selling shops in Diagon Alley.
Another way is to have the kitten be a gift from a mysterious character. Maybe Dumbledore gives a kitten to Harry as a way to help him deal with the stress of fighting Voldemort. The kitten could have some sort of calming magic that helps Harry stay focused and centered during difficult times. This would add an interesting dynamic to their relationship and also give the story a new angle to explore.
One way is to have a crossover where the technology of transformers somehow enters the wizarding world. For example, perhaps a magical experiment gone wrong causes a transformer to appear in Hogwarts. The students might be both amazed and a bit scared at this mechanical being. It could also be that a wizard or witch discovers a way to use transformer parts to enhance their magic, like using a transformer's energy source to power a particularly large and complex spell.