Place the garlic cloves and salt in a food processor and process, stopping several times to scrape down the sides, until finely minced.
With the food processor running, slowly drizzle in about 1/2 cup of oil. Stop to scrape down the bowl. Continue processing by drizzling in 1 tablespoon of lemon juice followed by another 1/2 cup of oil. Continue alternating lemon juice and oil until all ingredients are added, taking care to process thoroughly after each addition and stopping to scrape down the bowl frequently.
Continue to process until the mixture is totally emulsified and you have a smooth fluffy sauce. Store covered in the fridge.