Either way you should expect to pay half of it. If he offers to take your share it will be a pleasant surprise instead of an expectation and if he doesn't you won't be disappointed. Oh and don't think him not doing it says much about his character. For all we know he could have asked around on gag and had some guys tell him that 50/50 is the current standard.
I'd say bring your wallet so you don't seem presumptuous and then if he pays awesome if not you have money on hand. Most likely if you try to pay for yourself he will turn you down at least thats what's happened in my experience
I say you offer to go halfsies on the bill or just ask for your things to be on a separate bill. As time goes on he'll probably feel more inclined to pay for things but since it's just lunch I don't think its a big deal if you pay for your meal.