In medium bowl, combine yogurt, sour cream, cucumber, 2 tablespoons feta cheese, dill and ½ teaspoon garlic; salt and pepper to taste. Set aside.
In another medium bowl, combine lamb, egg, remaining feta cheese and remaining garlic; salt and pepper to taste. Form into 4 oblong burgers.
Prepare grill to medium heat. Grill burgers, turning once, to internal temperature of 160°F.
Place pitas on grill to crisp, turning once (about 1 minute). Place burgers in pocket of pita and top with cucumber sauce, lettuce, tomatoes and onions.