Dunno... I normally keep it closed so the toddler doesn’t throw unflushable things in it.
See? There are good reasons for certain things, but if there are not toddlers on the scene, then things like up or down shouldn’t matter.
</soap box
Actually, when I lived in the tenements, I had a dog whose rubber bone bounced off one of her fangs and jumped into the commode when flushing commenced. Had to call Roto Rooter. Could ill afford it. Since then, keep the lids down. It's not a male/female thing, it's an economic, budgetary concept.
Now, where's the beer? The celebration needs commencitating.