recipe for lebanese style garlic sauce?

Re: recipe for lebanese style garlic sauce?

This is what I found for lebanese garlic sauce:

1 head of garlic, separated & peeled
1/8 c lemon juice [up to 1/4 c]
1/2 - 1 tsp kosher salt, not regular small grained
1/4 - 1/2 tsp sugar
1/4 c mild olive oil
1/4 c vegetable oil

thickening agents:

1 very small floury potato OR
mayonnaise (LOTS) OR
bread soaked & squeezed dry

Procedure: Is that my buréka?: thoum — aïoli’s lebanese cousin