The lamb and chicken can be marinated up to one day in advance and refrigerated. Remove from the fridge one hour before grilling.
Combine 1/2 cup yogurt, oil, lemon zest and juice, coriander seeds, and paprika in a bowl; add 1 1/2 teaspoons salt and 1/2 teaspoon pepper. Mix well. Divide mixture between 2 resealable plastic bags; add lamb to one and chicken to the other. Seal bags after removing any air; massage meat to evenly distribute marinade. Let stand at room temperature 1 hour, or refrigerate up to 1 day (remove 1 hour before grilling).
Thread meat onto long metal skewers (or soaked wooden skewers) with a lemon quarter on each end, leaving 1/4 inch between each piece to ensure even cooking. Thread tomatoes and onion onto separate skewers, then brush with oil. Season meat and vegetables with salt and pepper. Stir together remaining 1 1/2 cups yogurt, feta, and 1/2 teaspoon salt. Transfer to a serving bowl; drizzle with oil and sprinkle with pepper.
Preheat grill for direct-heat cooking (medium-high on a gas grill). Brush grates with oil. Grill chicken until just cooked through, 10 to 12 minutes. Grill onions, turning a few times, until charred in places and softened, 8 to 10 minutes. Grill lamb, turning a few times, until charred in places, 6 to 8 minutes for medium-rare. Grill tomatoes until charred in places, 4 to 5 minutes. Transfer meat and grilled tomatoes and vegetables to a serving platter. Grill pitas, flipping once, until charred in places, 1 to 2 minutes; immediately wrap in a clean kitchen towel to steam and soften until ready to serve.
Serve meat, onions, and tomatoes with pitas, yogurt sauce, cucumber, and dill, with grilled lemon wedges alongside.