For the tzatziki sauce, mix together the Greek yogurt, garlic, lemon juice, grated cucumber, dill and salt. Cover and refrigerate until ready to use.
Heat grill over high heat. In a large mixing bowl, gently fold the ground lamb, garlic, feta, mint, oregano, salt, pepper and crushed red pepper flakes just until combined.
Now it's time to make the ground lamb patties. Evenly divide ground lamb mixture into four balls and form into 4-inch patties.
Place burgers on hot grill. Cook for two to three and a half minutes on one side, depending on desired doneness, and then flip and cook for the same amount of time.