In the bowl of a food processor, add the egg yolks, vinegar, water, and mustard. Turn the food processor on and pulse to combine.
With the motor running, slowly drizzle the oil, a few drops at a time, through the feed tube. Eventually the mixture will begin to thicken. Continue to slowly drizzle in the oil until you’ve achieved a thick, creamy consistency (you may not need all of the oil).
Add the salt and lemon juice and pulse to combine. Stir in more salt and lemon juice to taste, if desired.