Combine the yolk, salt, water, and lemon juice in a 2.5-quart bowl. Fold a hand towel into a ring on the counter and set the bowl in this ring to hold it steady while you whisk. Using a sauce or balloon whip (whisk), stir the ingredients together.
Add the oil slowly while whisking vigorously. It helps to measure out your oil into a cup that pours well in a wire-thin stream; alternatively, you can start your emulsion by drizzling the oil off a spoon, then pouring the oil after the emulsion has begun. Add a few drops of oil as you begin to whisk; when the emulsion becomes creamy, you may increase the speed with which you add the oil to a thin stream. From the beginning the mixture should be thick enough to hold its shape and look luxuriously creamy. Add the oil too quickly and it will break, that is, it will turn soupy. When all the oil is incorporated, add additional lemon juice to taste. If the mayonnaise is too thick, it can be thinned by whisking in a little water.
If it breaks, put a teaspoon of water in a clean bowl and start the process over by drizzling in the broken mayonnaise while whisking.