There was one at the southeast corner of I-35 and 290 for a while - Pyramids, maybe? It's been a while since I ate there and I don't go by that intersection unless I really have to so I don't know if it's still in business.
Having said that, my Lebanese friend likes Ararat and Phoenicia although Phoenicia is more of a bakery than a restaurant.
Is Longhorn Po-Boy's still around? How about Marrakesh on Congress?
There's a new place out on North Lamar past Parmer called Byblos that's very good. Authentic Lebanese food. My dad (100% Leb.) gives it his seal of approval. He also likes that Pyramid place someone above mentioned.
Traffic - After I wrote that I thought the same thing....I was trying to contrast Persian food from what is traditionally known as middle eastern food.
As for whether Persia (Iran) is part of the middle east, I think you'll get differing views from Persians than you would the rest of the world.