TZATZIKI: In a medium bowl, combine cucumber, yogurt, lemon juice, mint and garlic; season with salt and pepper. Cover, and refrigerate until ready to use.
BURGERS: Heat grill or grill pan to high. In a medium bowl, use a fork to gently combine lamb, onion, parsley, and oregano; season with salt and pepper. Gently form mixture into 16 small patties, about 3/4 inch thick. Grill until medium-rare, 2 to 3 minutes per side.
To serve, warm buns on the grill or directly over a gas burner, turning once. Fill with lettuce, mini burgers, tomato, and tzatziki.