First dates and alcohol — a big no-no!
It doesn’t matter that you are both adults — it doesn’t matter that it’s just lunch — it doesn’t matter that there are plenty of other people around — it doesn’t matter that it’s daytime. Whenever you are on your first couple of dates with someone new, you should avoid situations where alcohol will be a big part of the picture. Booze parties and the like should not be the venue for your first date — you can save that stuff until you are more serious about that person, and more secure in their presence. The presence of alcohol can lower emotional conditions and set you up for all sorts of trouble and problems — now and later.