Good Morning and Happy Monday!
Business lunches are very common these days, (I had one with a bride a few weeks ago) and a great way to get business accomplished and get to know clients and colleagues too.
I think the question of who pays is probably the most prevalent one concerning lunches. Like other outings, who ever does the the inviting should offer to pay. Be prepared with appropriate methods of payments and for your guest to offer to pay their own way. Avoid excessive arguing over the check, offer to pay and if your guest refuses, offer once more and then drop it.
Remember to execute proper table manners and always arrive a few minutes early. If you tend to be indecisive, preview the menu online and have an idea of what you’d like to order.