Do you mind treating me to lunch? is correct.

"Would you mind" would be more polite for a request. The normal context would most likely be that you're asking a favour because you either can't afford to pay for yourself or haven't got your credit card on you. "Do you mind doing something for me" would be used if you suspected the other person may not want to do it.

The first is correct but it isn't something you would normally say. If someone is treating you to lunch you would express gratitude. Another possibility would be to say "you really don't need to do this." But "do you mind treating me" sounds a little bit like "I hope you aren't upset about treating me". It's an odd thing to say, though there might be some circumstances in which it would be appropriate.

Do you mind treating me lunch?