Actually, some AA FA's *DO* do lavs, whether they're required to do so or not.
I was on Monday's ORD-SFO mid-afternoon 767 (sitting in the coach "business class" section), and the one loo at the back center had been disgustingly littered with paper towels all over the place. (Beats me what the occupant had been up to, or what barn s/he was born in). As I got up to go there, the FA said "if you can wait just a second, I'd like to try and tidy up in there..." and picked it all up. As she emerged with a plastic bag, I said "it takes all kinds" and she smiled and said "not everybody's as polite as they should be."
It was a nice professional touch by somebody who seemed to care about the product. I'm sure they don't have to, but here, at least, was somebody who wanted things presentable.