There are two new-ish lunch options for Penn Quarter, located within one block of each other.
District based Taylor Gourmet already had a Philly-style deli at nearby City Vista (485 K St NW). But, that's a bit of a walk if you're in Penn Quarter and you need a quick lunch. The Taylor folks recently opened a new restaurant at 624 E Street NW, about half way between the Navy Memorial and Verizon Center.
Taylor has all manner of sandwiches including five vegetarian options. None are vegan as-is, though. The prices are good. A six inch hoagie with soda and chips will set you back about $10, the magic lunch number. The staff at Taylor are always so nice and they keep the line moving. I love them because you get your sandwich quickly and roll out.
Just a block south of Taylor is Protein Bar -- 398 7th St NW. This place is awesome. There are only two locations outside of Chicago and one of those is in the District (with another on the way to 19th & K NW). The Penn Quarter location has been open since July of last year.
Protein Bar is what I'd consider a fast casual style restaurant with healthier options than others in this category. They are very vegan friendly. There are several menu items (breakfast, burritos, salads, chili) that can be ordered vegan right off of the menu. In addition you can modify most dishes into vegan meals.
The raw juices and specialty blended drinks cost a bit more, but a wrap or salad plus a bottled drink comes in right around $10. Really, really into this place and will definitely be back.