The "who pays" question is easy enough, imo. I offer to pay. One, I offer to pay for lunch with friends anyway, so it's not some special antiquated courting ritual, it's just a pleasantry I don't mind extending. I'm by no means loaded, but I *do* work a lot, so consequently I tend to be much less strapped for cash than my peers, so I go ahead and offer to pick up the tab.
And then let's look at the practical side. Frankly, I think anyone who's going to get angry at someone offering a free lunch - and I do mean a free lunch, not that "lol I paid for dinner now I'm going to press you into sexual favors" bullshit some guys our age do - is petty and ridiculous, and certainly not someone with whom I want to be involved in any capacity anyway. Like I said, friends or dates or lovers, I pay pretty regularly anyway... I don't have the time, patience or energy to get in fights over petty shit like that on a regular basis. So it's a nice filter.