Step 1Heat the broiler. Place the peppers on a rimmed baking sheet skin-side-up. Broil until the skin is blackened, 8 to 10 minutes. Wrap in damp paper towels and set aside while you make the sauce. Turn the oven to 250 degrees. Wrap the pitas in foil and warm in the oven.
Step 2Meanwhile, combine the yogurt, mayonnaise, lemon zest and juice in a bowl. Trim the ends of the cucumber. Use the coarse side of a box grater to grate about 1/3 of the cucumber, including the peel. Without packing it, measure 1 cup. Grate more if needed. Mix the grated cucumber, mint and salt into the yogurt mixture. Add pepper to taste. Set aside.
Step 3Cut the rest of the cucumber into 2-inch-long matchsticks. Scrape the skin off the peppers and cut into thin strips. Mix the cucumber, peppers and lamb in a large bowl. Add 2/3 cup of the sauce and gently mix. Fill each pita half and serve immediately. Serve the sandwiches with crudites (raw veggies), using the extra sauce as a dip.