In a large sauce-pan bring to a boil the 6 cups of broth. Add the rice and simmer for about 20 minutes until tender. Reduce the heat and barely simmer. in a mixing bowl beat the eggs until they are light and frothy and stir in the lemon juice. Slowly add 2 cups of the broth to the mixing bowl, beating constantly. Stir the mixture gradually into the remaining broth. Reheat the soup before serving, but do not let it boil.