In a bowl, combine the ground beef, onion, mint, lemon zest, 3 tablespoons of the yogurt, 1/2 teaspoon cumin and 1/8 teaspoon salt. Form into 12 2 1/2-inch patties, and thread onto bamboo skewers; chill until ready to cook.
For the raita, In a small bowl combine the cucumber, carrot, cilantro, sugar, the remaining yogurt, 1/4 teaspoon cumin and 1/8 teaspoon salt.
Preheat a large, non-stick skillet over medium-high heat. Working in batches, place the beef skewers in the skillet and cook for 5 to 6 minutes or until internal temperature reaches 160° F, turning once. Serve alongside the raita.
Skewer the beef patties after they're cooked.