Make sauce: Stir yogurt, sour cream and lime juice in a bowl until blended. Add garlic, cumin and parsley; season with salt and pepper. Serve at room temperature or cover and chill.
Make kebabs: Prepare a charcoal fire and let burn to a gray ash. Toss lamb with cumin, salt, pepper and oil. Thread lamb onto 8 metal skewers, dividing evenly and alternating with eggplant, peppers and tomatoes.
Brush kebabs with oil; season with salt and pepper. Set grill 6 inches from heat. Grill, turning, until lamb is browned and firm, 12 to 15 minutes; serve warm.