Mix all of the ingredients together and refrigerate. Marinate at least one hour up to 24. Heat a skillet with oil over medium high-high heat. When the oil shimmers add the lamb to the skillet. Brown on all sides and set aside.
Combine all ingredients and refrigerate until ready to use.
Warm the pita in the oven or skillet. Spread cucumber yogurt on one side. Top with greens, lamb, cucumber, tomato, red onion, feta, and mint. Drizzle with olive oil and serve with lemon wedges.