Hi !
Wasn't here for some time, so will try to catch up to what I missed.
OK, so no idea if you are still here, but we can develop that a little if you want.
From what I remember the Lunar Mansions were just changing day by day from 1 to 28, but if we check how they show up in calculators it did seem to be just 1 a day, wasn't directly connected to the Moons movements I think, even though that is around 28 as well, but not exactly.
They can be added to places, here for example:
https://bright-hall.net/astrocalc/But I never found good practical steps of using them, are you using them with some system or something?