Nope. I always closed the entire lid. Why? Because I complained all the time about the crap all over the sink and said it's going to end up in the toilet when you leave the lid up while I'm trying to shave or brush my teeth.
That exactly happened too. I walked out of the bathroom and went to work leaving one of her makeup brushes down in the toilet for her to see where it got knocked off the sink and landed in the toilet.