For Lincoln in this crossover, you can focus on his resilience from 'No Such Luck'. Despite all the bad luck he had, he still tried to keep a positive attitude. In the crossover, put him in difficult situations where he has to use that same tenacity. For example, if they cross into a dangerous new world, he could be the one motivating the others.
Luna could use her musical talent in a unique way. Maybe in the crossover world, music has a different power. She could be the one to discover this and use it to help the family. Her carefree and creative personality would shine as she experiments with this new form of music. It would show how her character from 'Loud House' adapts to the crossover scenario.
How about a character from a classic fairy tale? For instance, Cinderella could be accidentally brought into the 'The Loud House' world during the crossover. Her presence could contrast with the chaos of Lincoln's bad luck. She might try to use her positive attitude and her experience with hardships to help Lincoln deal with his situation.
Another plot might involve a character from the 'bad luck' side of the crossover coming to the Loud House world and bringing their bad luck with them. This could disrupt the normal family dynamics. The Loud siblings would then have to figure out how to get rid of the bad luck and restore order. They might try all sorts of wacky plans, like using their own unique skills and talents in a new way to combat the bad luck.
One idea could be a crossover with another popular animated show. For example, the characters from 'Loud House' could end up in a different universe where they have to use their unique skills from 'No Such Luck' to survive. Maybe they meet characters who have similar family dynamics but different challenges.
One idea could be that the misfortunes from 'No Such Luck' somehow cross over into an alternate universe in the crossover. For example, Lincoln's bad luck could start affecting the other characters from the crossover world in strange ways, like causing their gadgets to malfunction.
If you're doing a crossover with 'Scooby - Doo', Scooby and Shaggy are must - includes. They could bond with the Loud family over food and then get caught up in a mystery in Royal Woods. Velma could use her smarts to solve the mystery, and Fred could lead the way with his trap - making skills. Daphne could also befriend the Loud sisters and add some charm to the story.
Leni and a bad - luck character who is always in a hurry to fix things but just makes them worse. Leni's somewhat oblivious but kind - hearted nature could either be a hindrance or a help. They could get into all sorts of misadventures together, like trying to fix a fashion disaster that the bad luck caused, but instead creating an even bigger mess.
One idea could be that the Loud family somehow gets transported to Gotham City. Lincoln could befriend Robin and they team up to solve a mystery that involves both Gotham and Royal Woods' villains. Maybe the Joker has a plan that involves stealing a special item from Royal Woods, and the Louds have to work with Batman to stop him.
In this crossover fanfiction, the Hulk's strength could be used to help the Loud family in a big way. For example, there could be a natural disaster about to hit Royal Woods, like a huge flood or an earthquake. The Hulk, with his superhuman strength, could hold back the floodwaters or stop the shaking ground. Meanwhile, the Loud kids could be helping the townspeople evacuate. It would be a story of how two different universes come together to save a town.
One example could be a crossover where the characters from 'The Loud House' meet the characters from 'IT' in a strange town. Maybe the Loud siblings end up in Derry and have to face Pennywise together with the Losers Club. It could be interesting to see how the different personalities from 'The Loud House' react to the terrifying situations in 'IT'.