Preheat the oven to 450 degrees F. Line a baking sheet with parchment and coat with cooking spray.
Cook the spinach in a large bowl in the microwave according to the package instructions. Let cool slightly.
Add the turkey, breadcrumbs, cumin, garlic, carrot, egg, 1 tablespoon of the dill, 1/2 teaspoon salt and a few grinds of pepper. Mix with your hands until just combined. Scoop mounds of the meat mixture (about 2 tablespoons each) onto the prepared baking sheet. With damp hands, roll the mounds into balls and space them evenly apart on the baking sheet. Bake until cooked through, 12 to 14 minutes.
Meanwhile, stir together the yogurt, lemon juice and remaining dill in a small bowl. Season with salt and pepper.
Serve 3 meatballs in each pita half. Pack in shredded lettuce and sliced tomatoes. Drizzle with the yogurt sauce.
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