Lightly beat the eggs in a large bowl and set aside. Boil chicken in the broth and water until chicken is fully cooked, about 20 minutes depending on the size of the breasts and whether or not you leave it on the bone or not. Remove the chicken from the broth, let cool a bit and then using two forks, shred the chicken. Meanwhile, add lemon juice to the the broth mixture and gradually add the broth to the eggs, stirring constantly with a whisk. Return the broth to the pan. Cook until slightly thick, about 15 minutes, stirring constantly. Season with salt and pepper and serve with lemon slices.