Break lettuce into bite-sized pieces into a salad bowl.
Put eggs into top part of a double-boiler. Whisk together. Add water, vinegar, and onions. Heat-stir over simmering water until thickened. This will take about 10 minutes. (If you have a small enameled saucepan, this sauce can be made directly over very low heat in just a few minutes. Make it first in a