Lucky Slice is definitely vegan-friendly. They don't do vegan pizza by the slice every day, only on Tuesdays. I've had it though and it's pretty tasty. However, you can order a whole vegan pizza anytime. When I asked which sauces were vegan, the guy working the counter went and got their recipe book and went through THE WHOLE menu with me, telling me which things were vegan and which things weren't.
-Red (fresh tomato, garlic and herbs)
-BBQ (sweet-n-tangy southern bbq)
-Herbal (fresh herbs, garlic, olive oil)
-Thai Peanut (Thai influenced peanut sauce)
Their balsamic salad dressing is also vegan.
I have yet to order a whole pizza from them, but I always go on Tuesdays for their vegan tapenade by the slice. I'll update when I do end up ordering a whole pizza.
They also do vegan bread sticks. They don't have them on hand, but they'll make them to order. I order them all the time, they're really good. You can also get a sauce with them for dipping.
It was so amazing to encounter someone so helpful and willing to figure out which things were vegan. I would definitely recommend this place to anyone.
Updated from previous review on Wednesday May 28, 2014
Cons: vegan pizza by the slice only on Tuesday