One way to blend the themes is through the idea of sacrifice. In LOTR, many characters sacrifice for the greater good, like Boromir. In Narnia, Aslan sacrifices himself. A fanfiction could explore how characters from both worlds understand and are affected by sacrifice. Also, the theme of the power of nature is present in both. The ents in LOTR and the talking animals and plants in Narnia can be part of a story that shows how nature can be a force for good against the encroaching evil in both worlds.
One idea could be to have the characters from Narnia and LOTR meet in a magical realm that exists between their two worlds. For example, Frodo and the hobbits could encounter Aslan. Another could be a story where the One Ring somehow ends up in Narnia and the Narnians have to deal with its corrupting influence, while Aragorn and his companions come to Narnia to help. Maybe the White Witch could team up with Sauron, creating a more powerful and menacing villain for the combined forces of Narnia and Middle - earth to face.
Another plot could involve the Rings of Power in LOTR having some sort of connection to the magic in Narnia. For example, the White Witch might be interested in obtaining the One Ring to increase her power. This could lead to a conflict where the forces of good from both Narnia and Middle - earth have to join together to stop her. The different races in both worlds, such as the hobbits, dwarves, elves in LOTR and the talking animals in Narnia, could interact in unique ways during this conflict.
I think Lucy from Narnia and Frodo from LOTR would make an interesting pairing. Lucy has her own kind of innocence and faith, which could be a contrast to Frodo's burdened and determined nature. She might be able to offer him a different perspective on his quest, and he could show her the more complex and dangerous world of Middle - earth.
One idea could be that the One Ring somehow ends up in the world of Pirates of the Caribbean. Jack Sparrow, being the wily character he is, gets wind of its power and decides to either use it for his own gain or sell it to the highest bidder. The Fellowship, in turn, has to track it down in this strange new world full of pirates, sea monsters, and cursed treasures.
Definitely Legolas and Will Turner. Legolas with his amazing archery skills could teach Will some new techniques, and Will could show Legolas the ropes of being a pirate. They both have a sense of honor and loyalty, so they would make an interesting duo.
A lesser - known but excellent piece is 'Ringbearer Buffy'. Here, Buffy is somehow made into a ringbearer. It's a unique take on both franchises. The story delves deep into how Buffy's personality and her experiences as a slayer would affect her role in the quest to destroy the One Ring. It has some great character development and some really intense action scenes.
In a Harry Potter and LOTR crossover fanfiction, black magic could take on different forms. In the Harry Potter universe, it's often associated with the Dark Arts like the Unforgivable Curses. In LOTR, dark magic is related to Sauron and his minions. A crossover might explore how wizards from Harry Potter's world react to the more ancient and malevolent black magic of Middle - earth.
Sesshomaru's speed and agility would be a great asset in Middle - earth. He could easily outrun orcs and other foes. His sword, Tenseiga, which has the power to resurrect, could also have an interesting impact. For example, if he were to use it on a fallen hero, it could change the course of a battle.
One interesting idea could be a crossover with a modern - day superhero universe. Imagine the Narnians having to team up with superheroes to fight a common enemy that threatens both worlds. Another idea might be a crossover with a classic fairy - tale world like Wonderland. The different rules and characters from each world interacting would create a really unique and fun story.