The Lady's Quarters is where The Lady thrives. This is the last chapter of the game, not including the DLCs as those are from The Runaway Kid's point of view.
Appearance
It appears to be a small house, in which The Lady lives. It is rather lavish when compared to the rest of The Maw, featuring lush purple carpeting/wall paper, decent furniture and flooring, and clean interior. This is also where The Lady chases Six in the last chapter.