To prepare sauce, combine the first 5 ingredients in a small bowl; cover and chill until ready to serve.
To prepare sandwiches, heat a large nonstick skillet over medium-high heat. Add lamb and beef to pan; cook 5 minutes or until browned, stirring to crumble. Drain well, and set aside. Wipe pan with a paper towel.
Lightly coat the pan with cooking spray; return to heat. Add onion; sauté 3 minutes or until tender. Stir in meat mixture, thyme, ground cumin, 1/4 teaspoon salt, crushed red pepper, and garlic. Reduce heat to low; cook for 2 minutes, stirring occasionally. Remove from heat; stir in parsley. Fill each pita half with 1/4 cup lamb mixture, 2 tablespoons cucumbers, about 1 tablespoon roasted peppers, and about 1 tablespoon sauce.