Mix together lamb, onion, olive oil, cumin, 1 tsp. each salt and pepper, and cinnamon. Let stand for 15 minutes.
Make sauce: Combine yogurt, mint, garlic, lemon juice, and 1/4 tsp. each salt and pepper.
Preheat broiler to high and place rack 2 inches from heat source. Thread lamb tightly onto metal skewers. Place on broiler pan and broil, turning once, until well-browned but slightly pink within, about 6 minutes total for medium (cut a piece open to test). If you prefer medium-well, cook for 8 minutes; for well-done, cook for 10 minutes.
Serve immediately, accompanied by yogurt-mint sauce.