Granted, I've only been there twice, but I can tell you LMaD is set up literally right next to TPiR. You enter the studio
from the west side of the building, pass by LMaD - which takes up the entire west half, there's an "alley" where there's crew present, along with an area for the models, and then you hit the TPiR set, which presumably takes up the entire east half.
Office space, dressing rooms, etc. run the entire length of the building on the south side.
Due to the way it is set up with no wall, there is no way both shows could be filmed at the same time. Additionally, it is my understanding that there is a shared control room.
The LMaD set was clearly decorated for the previous season, as Wayne Brady was on a taping break to do Broadway, so it did not appear as if it had been touched for a while. My guess is that they do not strike the sets, and if they do, it's very rarely. Somebody had recently complained on /r/thepriceisright that there was clearly dust on several of the TPiR set pieces...