In a glass bowl, whisk together the egg yolk, salt, mustard, and sugar. Combine lemon juice and vinegar in a separate bowl, then put the oil in a plastic squeeze bottle.
Whisk half of the lemon juice mixture into the yolk mixture. On a nonskid pad, whisk briskly, adding the oil a few drops at a time until the liquid seems to thicken and lighten a bit, which means you've got an emulsion on your hands. Once you reach that point, you can relax your arm a little and increase the oil flow to a constant, but thin stream. Once half of the oil is in, add the rest of the lemon juice mixture.
Continue whisking until all of the oil is incorporated. Store in a large container with a lid. Leave at room temperature for 1 to 2 hours, then refrigerate for up to 1 week.