Another theme is the power dynamics. Given Lucifer's status as a fallen angel and his powers, how does his relationship with his wife (the OC) affect or change the power balance? For example, does she gain some powers through their connection? Or does she help him control his more devilish tendencies?
You can start by looking on fanfiction websites like Archive of Our Own (AO3). It has a large collection of fanfictions, and you can simply search for 'Lucifer Morningstar wife OC' in the search bar. There are often filters you can use to sort by popularity, rating, etc.
It shows his vulnerability. Usually, Lucifer is seen as this powerful, menacing figure. But when he cries in fanfiction, it reveals that he has emotions and can be hurt.
Lucifer in this fanfiction could be depicted as a complex character. He's likely to be extremely powerful, with a commanding presence. His intelligence would be sharp, always strategizing and thinking several steps ahead.
Power is a major theme. Two Lucifers would bring a lot of power into one story, and it can be about who has more power or how they use their power together.