Commodes have "two" lids!

I need some clarification on how one must leave the lids positioned on toilet commodes when finished with them.

In a ball park, for instance, where there are ladies and men's toilets, I would have to assume that in the men's toilets most men use the urinals for urination, which have no lids.
And, in the ladies toilet everything is sit-down commodes where one lid is up and the other is down!
The rib seems to be, that of being at home, where there are no urinals--why, I don't know unless there isn't room for one!
Now the question is, what does a woman do with the lids when she leaves the toilet, and what does a man do?

Or is their an accepted formality to it, or is it understood that whatever the women want is what should be done?

Maybe philosopher Muddle could enter in on this one to clear up the thing?
Denise would simply not be opened minded!