In small bowl, mix sauce ingredients. Cover; refrigerate until ready to use.
In large bowl, mix burger ingredients until well mixed. Shape beef mixture into 16 patties, about 1/4 inch thick.
Place 8 patties in 12-inch nonstick skillet; cook over medium-low heat about 3 minutes. Turn patties; cook 2 to 4 minutes longer or until meat thermometer inserted in center of patties reads 160°F. Remove patties from skillet; cover to keep warm. Repeat with remaining patties.
With serrated knife, cut pita breads in half horizontally. Place patties on bottom halves of breads. Top each patty with about 2 teaspoons sauce, several slices of cucumber and strips of onion. Cover with top halves of breads. Serve immediately.