Hi catroast, This recipe is a garlic sauce but not the original lebanese recipe.
My wife ordered a book she saw on the internet called Classic Lebanese Cuisine by Chef Kamal who was a caterer in washington DC and now lives in California.
Here's a link to his video on how to make garlic sauce. The real deal doesn't even use eggs by the way. You also don't use olive oil because it changes the taste and with our home experience made the "toom" bitter. Olive oil is better with aioli another kind of garlic sauce.
By the way I was told by some people working in fast food place that they will fake the recipe with mayo and also add potatoes to make the garlic sauce.
Do you mean the garlic mayo they have at fast food lebanese type places?
There is a large lebanese supermarket in Brossard, on Taschereau, who's name escapes me right now, that makes this type of sauce. Actually I think Adonis makes it as well.
Alternatively, you could go to any of the lebanese restos and buy their sauce separately. If it is not this style of sauce you are talking about, the lebanese supermarkets also make lebanese tzaziki-type sauce, that may be what you want. I would start looking at Adonis.