I generally close the lid all together when im done but in all honesty I think its b/c women dont have to worry about this in public the seats are always down in womens bathrooms. I dont see the point I think that men have just as much right to ask them to put it up when they get done to be honest but whatever keeps the relationship happy I guess.
personally I think it might be a sign of low IQ if you dont look before you sit anywhere for that matter...