Process garlic and salt in a food processor until finely chopped, about 30 seconds, stopping to scrape down sides of bowl as needed.
With food processor running, add ½ cup oil, first very slowly, adding a few droplets at a time, and then moving to a very thin, steady stream using a 1-tablespoon measure until a creamy sauce forms, 4 to 5 minutes, stopping to scrape down sides of bowl after each addition.
With processor running, very slowly add remaining 1 ½ cups oil in a very thin, steady stream using a liquid measuring cup, processing for 4 to 5 minutes; drizzle in lemon juice and 2 tablespoons cold water, and process until smooth.
