Yeah, I would prefer the lid down but I gave that up long ago. I'll settle for the seat down, and I get that about 75% of the time.
I always check.
AND WEAR SHOES.
Don't get me started!
Folks who want the lid down have that preference for different reasons - have you asked? If she's into feng shui, it's bad to have the lid open. All your chi goes down the toilet. For real. If you are into that, I mean. Others have dogs who drink out of the bowl and it squicks them out so they want the lid down. For others, it's kids. And as the above replies illustrate, there are some folks who just prefer it that way for hygiene or aesthetic or other miscellaneous reasons.