He has asked me to have lunch two times this month. Does he like me?

If he's getting that personal he is probably interested in a romantic relationship. He's been dropping you hints right and left. He meets ladies online, he talks about dating, about whether you have an ex, your relationship with your ex, whether you have kids, etc. He is sizing you up as a potential date and it sounds like you passed the first round interview! The ball is now in your court. You can meet him for lunch again, or not.