According to an article I read from The Capital newspaper in Annapolis, their food is "just naturally vegan." They are traditional 2000 year old recipes from Lebanon that were made out of necessity due to lack of refrigeration.
They serve, "homemade hummus, meatless stuffed grape leaves, spinach pie, mixed grilled vegetables and crunchy on the outside, but melt-in-the-mouth falafel balls." While it sounds like the restaurants are vegetarian heavy (or all-vegetarian?), they are not completely vegan or dairy-free, so keep an eye out for yogurt or butter usage. Nonetheless, they do offer a vegan baklava!
Check their website for locations, hours, and the menus: www.lebanesetaverna.com