Well, 'Love in the Courtroom' is another great one. It combines the courtroom drama aspect that is so characteristic of the Phoenix Wright series with the budding relationship between Phoenix and Iris. The fanfic is full of suspense, just like in the games, and at the same time, it weaves in the romantic elements very skillfully.
To develop Professor Layton, you can focus on his intellectual side more. Show how he analyzes every situation and how his vast knowledge helps him make decisions. For Luke, you can show his growth. Maybe at the start he's a bit timid in solving really difficult puzzles, but as the story progresses, he becomes more confident. For example, you can have a scene where Luke is the one who figures out a crucial puzzle all by himself.
One idea could be that they go on a journey to a mysterious land that's not on any map. In this land, they encounter strange creatures and have to solve puzzles that are based on the unique culture there. Another could be a time - travel plot where they end up in the past and have to figure out how to get back while also helping the people of that era with their wisdom. Maybe a third idea could be that Luke gets kidnapped and Professor Layton has to use all his skills and knowledge to rescue him, facing many challenges along the way.
One common theme is growth. Luke's growth as a character, both in intelligence and in his relationship with Professor Layton. Another theme is mystery - after all, they are known for solving mysteries in the original games.
Courtroom drama is another prevalent theme. The reader might be a witness or somehow involved in the courtroom scenes with Phoenix. This allows for exciting interactions and plot developments within the legal framework that is so characteristic of the Phoenix Wright series.
To make the fanfic more interesting, you can add other elements. For example, include other characters' reactions. If Pearl is around, how does she react to Maya tickling Phoenix? You can also set it against a backdrop of a specific event in the Phoenix Wright universe, like right after a big trial victory. This gives more context and depth to the story.