J, depending on how you draw the boundaries, the north side can encompass 40, 50 square miles -- an idea on your travel limits might prod readers' memories. (I'm not sure, myself, that I get the distinction between lunch choices and lunch options either.)
I haven't eaten at the aforementioned Sue Van's in a year or so, but I've liked it since it opened shortly after I moved here, and I think it might meet your qualifications.
In Andersonville, you might try A Taste of Heaven or Kopi Cafe. The former bakes its own bread. A little further east, on Bryn Mawr near Broadway, Flourish also makes its own sandwich breads, although I don't know whether they bake from scratch or not. And a block east of that, the Bryn Mawr Deli has some sandwiches.
Also, on the stretch of Damen between Montrose and Foster, you'll find a variety of options, including diners, a number of coffeehouses with sandwiches (two with different menus devised by Mimi the Deli Queen, although she no longer works for either), and some very highly regarded Thai spots.
Again, the more you can help us help you, the better the information we can offer.