It always bugged me that they simply refer to her as "Lady". And then at about two in the morning when I was looking at my last beer, I realized: After they leave the North, they're no longer speaking the same language, so "Lady" would sound like a normal name to everyone they met, and not sound like the title that it started as. It only took about three months for me to figure it out.
It also helps that they drop the "The" after leaving the North. In the North she is "The Lady", her title. In the South she is just "Lady", a name.
Actually, it's not a fridge trope, since it is explicitely described in the book.