We at twice at Lebanese Restaurant on a recent visit to Phuket, and both times found it to be a good option for dinner (when the vegetarian restaurants in town are usually closed).
The menu here offers about half a dozen veg*n (or veg*nizable) options. We had the hummus, felafel, mashed eggplant (ordered without yoghurt), and stuffed grape leaves, and we found all of them to be fresh and tasty. In fact the felafel was unusually light (not oily) and enjoyable.
Service was casual but fine. We'd suggest placing your order with one of the older proprietors, as the young locals didn't seem comfortable with English and we weren't sure if they understood our request for no yoghurt, whereas the guy who seems to be the boss speaks good English and was helpful.
Prices were a little on the high side considering the smallish portions, but it's still one of the better veg-friendly options in town so we'd go back again.
Cons: Serves meat, a little on the pricey side