1. Place first 10 ingredients in a food processor; process until smooth. Place breadcrumb mixture in a bowl; add lamb, beef, and feta, stirring gently to combine. Shape mixture into 12 (2-ounce) patties. Refrigerate 10 minutes to set.
2. Heat a large nonstick skillet over medium-high heat. Add 6 patties to pan; cook 4 minutes on each side or until desired degree of doneness. Remove from pan; repeat procedure with remaining patties.
3. Place 1 lettuce leaf, about 4 cucumber slices, and 2 lamb patties in each pita half.