Preheat a grill to medium-high.
In a medium bowl, mix the yogurt, spices, dried and fresh herbs, and lemon juice. Add the meat; toss to coat. Thread the meat onto metal skewers. Thread the peppers and onion onto separate metal skewers.
Spray the peppers and onions with cooking spray; season with salt and pepper. Grill, turning occasionally, until the vegetables are crisp-tender and browned in spots, 10 to 15 minutes.
Brush the grill with vegetable oil. Grill the meat, turning often, until cooked through (for chicken) or medium doneness (for lamb), 12 to 15 minutes. Grill the halved lemon, cut side down, until charred, about 5 minutes. Douse the skewers with the grilled lemon's juice.
Grill the bread until blistered, about 1 minute per side. Slide the meat and vegetables off the skewers into a large bowl; toss together. Make wraps by filling the bread with the grilled meat and vegetables, lettuce, tomatoes and giardiniera.