My first ever trip to Dortmund has had both good and bad points. Kartoffel-Lord is most certainly one of the good ones. As I write, I have visited twice in 24 hours.
The restaurant is fairly central, looks fresh and clean and has a friendly atmosphere. It's not too large and there is a steady flow of customers but both times I've visited I've been lucky enough to find a seat and enjoy my food without being hurried.
The Arabic appears to be the only vegan main but is delicious (as others have commented) and you can, of course, tell them if there are any vegetables you don't want in it as they make it fresh in front of you.
They serve a selection of drinks including Fritz-Kola, Bionade and beer and everything is very reasonably priced. Two of us had a wrap and a drink for about EUR 12.
Cons: Not all vegan :-)