Grate your cucumber, then let it rest in a colander to drain for about 10 minutes. Make sure to use paper towels or a tea towel to press out any leftover liquid.
In a small mixing bowl, stir the cucumber, yogurt, garlic, lemon juice, dill, and salt together. Set aside.
Lightly oil the grate of your outdoor grill, and preheat it to medium-high.
Season the burger patties with a sprinkle of Greek seasoning on each side.
Cook each patty on the preheated grill for four minutes. Flip, and grill the other side for four additional minutes. Place the burgers on a bun and layer with lettuce, onion, tomato, olives, and cucumber sauce. Enjoy!