Heat the chicken stock in a medium saucepan.
Meanwhile, melt the butter in a small frying pan, and stir in the flour. Whisk over medium heat until the mixture starts to brown. Add a few tablespoons of chicken broth to loosen the mixture, then pour the flour mixture into the pot of chicken broth, stirring. Bring to a boil, then turn off heat.
In another small bowl, beat the eggs. Put some of the chicken broth mixture into the eggs to temper them, then add the eggs to the broth pot, continuing to stir.
Now, stir in the lemon juice. Do not boil the mixture once you’ve added the eggs and lemon, but you can reheat it (stirring) before serving. Salt and pepper to taste.