Heat 4 tablespoons oil in a non-stick frying pan over medium heat. Add the celery, parsley, coriander and mint; fry for 4-5 minutes. Set aside.
Heat 4 tablespoons oil in a pot over medium heat. Add the chopped onions and saute until lightly golden. Increase heat to medium-high; add the beef and saute until brown on all sides. Add the turmeric powder and crushed tomatoes; mix well. Add 3 cups water. Cover the pot and bring to a boil. Reduce heat to medium-low and simmer covered for 30 minutes, stirring occasionally. Add the celery-herbs mixture, salt and pepper.
Cook covered over medium-low heat until beef and celery are tender (about 2 hours), stirring occasionally. Add more water during cooking, if necessary. Then add lemon juice and cook for 10 more minutes. Taste and adjust seasonings (add more salt, pepper or lemon juice if needed). Serve Khoresh Karafs with Persian Rice.