vegan-friendly near 40th and walnut?
I don't know how much of a real meal you want, but there is a Qdoba right there where you could definitely get a vegan burrito. There is also a Greek/mediterranean place on that street called "Greek Lady"... and Won's oriental... both of which I think should offer something vegan.
If you're willing to walk a little farther for something more interesting, up on 47th and Baltimore there are some Ethiopian places with good vegetarian offerings (I'm pretty sure there's no milk or egg in most of their food)... Dahlak is the one I'd recommend. If you haven't been up there before, I wouldn't walk alone even though it's probably fine.
Marathon (40th/Walnut) has some vegan options and it's got good people watching! Of course there's the Indian food palaces at 40th/Chestnut, cheap and absolutely vegan friendly. I like Tandoor, but try them all and see! There's tasty and cheap samosas ($.50 each, last time I was there) to go at the International grocery store on Walnut and 41st, just ask at the cash register.