I think that "Equal Rights" doesn't apply when dating, whether in the LS, or not. Even if I am asked out by a lady, I still make an honest effort to pick up the tab, if she insists, at least I have tried. I may be "old-fashioned", but I still strongly believe in "chivalry", which includes respecting my date, being a gentleman, and opening the car/building doors.
I can only speak for myself but when I go to a party with my BF I expect him to pay the party fee. My thought is that if he went as a single male (assuming it is a party that even allows single males) it would cost him a lot more. That said, if we go out to dinner I often pick up the tab and we usually split the hotel bill if we stay somewhere overnight. I don't expect anyone to pay my way just because I am a woman.