You may always feel free to inquire about lunch when the alternative would be eating in the Ministry canteen. As far as I am concerned, that is cruel and unusual torture.

(In all seriousness: as the beginning of the academic year approaches, I am spending most days at Hogwarts, and I am certain the elves would be happy to feed you as well. A pleasant hour's lunch and discussion of your studies would be an anodyne to some of the more tedious details of the Headmaster's role. I am otherwise spoken for on Fridays, but aside from that, you may feel free to invite yourself at any time; I will not need more than an hour's notice or so.)

And I keep meaning to mention -- while I will happily stand as your sponsor at Ourobouros in a year or two, doing so now would bring even more attention in your direction, and that sort of attention would not be the respect you have already earned with your skill, if you follow my meaning. Still: as a member I am entitled to more space in the changing-rooms than I am using, if you would like to store some of your things there and save yourself the trouble of a trip back to your apartment in the middle of the day.