In a medium size bowl beat your egg whites until light and frothy. You do not need to create soft peaks, you just want the egg whites frothy.
Add the egg yolks and continue to beat until incorporated.
While still beating the eggs, slowly add in the lemon juice.
While still beating slowly stream in the cup of broth that you have set aside. It should be warm (not hot). Continue beating until smooth all of the broth has been incorporated.
1 cup reserved broth (from meal you will be adding egg lemon sauce to)
Pour your avgolemono sauce into the pot with your meal. Carefully stir, or shake your pot, so that the avgolemono sauce gets incorporated throughout the meal.
Notes
The amount of lemon juice is open to adjustment depending on how tart, or not, you would like your avgolemono sauce.