Just to make sure i was clear on this however, we had prearranged to work together on it, and it was a class assignment at an event that was very very lowly attended. not sure if this makes any difference but i'm just clarifying.
Ah okay, well I mean thats different but I do think she likes you at least some from what you've said.
Go for it, you have nothing to lose. If she declines the offer, let it roll off your back and continue on. It's not a big deal at all, at least you gave it a shot and won't wonder what if.
I have a pretty good feeling she will say yes to getting lunch.