Speaking as someone with both small children and pets in the house, we always keep the lid down, too.

Having the lid down would be no problem for any woman, since the main concern is not the amount of work involved in raising/lowering the seat/lid, but rather the unpleasantness of accidentally sitting on the rim, combined with the possibility of falling in - rather hard to do with the lid down.<g> [My original response was in answer to the question, What is the big deal with having the seat up? If you're going to keep the lid up, please keep the seat down!]

"Hold on, my friends, to the Constitution and to the Republic for which it stands. Miracles do not cluster and what has happened once in 6,000 years, may not happen again. Hold on to the Constitution" - Daniel Webster