In a food processor, pulse garlic and salt until you get a smooth paste, scraping the sides of the bowl, occasionally. While the food processor is running, add the lemon juice. Pulse until fluffy. With the processor running, add 1/4 cup of the oil, in a thin and slow stream. Then, add 1 tablespoon of the ice water. Scrape the sides of the processor bowl and continue with another 1/4 cup of the oil. After each addition of 1/4 cup of oil, add 1 tablespoon of the ice water. Continue alternating until all the oil is used. Taste, adjust for sea salt, if necessary. You should have a light and fluffy sauce. The key is to add the oil very, very slowly.