i know we like to make the jokes about Maomao being like tang dynasty House and it is fun but i am currently watching house while i write and i can't help but think about the potential of interactions between Luomen and House, and heeeeeeear me out!
Luomen and House both kind of do the same thing of they have come to a conclusion and wont tell anyone, but will prompt and encourage their students to come to that same conclusion or get close enough. Maomao directly explains this in LN7, and while Luomen does it much nicer, its not like he doesn't do it. Luomen also does it with a smile and i can't say he doesn't tease Maomao as he watches her get to the answer, and that could be the familial relationship between them but also... kinda House vibes.
i also think Luomen would really pisses House off, because Luomen does not engage in the thing that House literally made his whole job. in never speaking on conjecture, Luomen refuses the idea and concept of the differential diagnosis, and we see this be an issue in 7 as well with the shrine maiden that leads to Maomao snapping at him. that is a very fun idea and concept to me like House pushing Luomen until he forces him to participate, only for it to probably still not work.
i also think House would be very pissed on Luomen's behalf re the whole eunuched and stolen knee thing, but mostly because he wants to prove that Luomen is also mad about this and it just isn't working.
...i think this would be a great rage bait for House, but also i think it might convince Luomen to do differential diagnosis's at least for his students and that is really fun.