Combine liver, brain, tongue, salt, and water in a large Dutch oven. Bring to a boil; cover and simmer 30 minutes or until meat is fork tender. Remove meat from broth. Cool; chop and set aside. Strain broth and set aside.
Sauté onion in butter in a heavy skillet until tender. Add chopped meat, dill weed, and pepper; cover and simmer 5 minutes. Add onion-meat mixture to reserved broth; cover and simmer 30 minutes. Add rice, and simmer an additional 20 minutes. Gently stir Egg- Lemon Sauce into simmering soup. (Maintain simmering temperature; do not increase heat.) Serve immediately.