For sauce, in a small bowl stir together yogurt and dill. Cover and chill until ready to serve.
Preheat oven to 350 degrees F. In a small saucepan bring the water to boiling. Stir in bulgur and 1/4 teaspoon of the salt; reduce heat. Simmer, covered, for 10 minutes. Remove from heat. Let stand, covered, for 5 minutes.
Meanwhile, in a large bowl combine onion, parsley, garlic, coriander, oregano, pepper, and the remaining 1/4 teaspoon salt. Add cooked bulgur and ground lamb; mix well. Shape meat mixture into six 1/2-inch-thick patties. Place in a shallow baking pan. Bake for 20 to 25 minutes or until meat is done (160 degrees F).
Place tomato slices (if desired) and burgers on bottoms of rolls. Add sauce and sliced cucumber. Replace tops of rolls.