Preheat grill to medium temperature.
In a bowl, combine cucumber, yogurt, lemon juice, mint and garlic to make a tzatziki sauce. Season with salt and pepper.
In another bowl, combine lamb, onion, parsley and oregano. Add salt and pepper.
From the mixture, form small burger patties (about 15 pieces), approximately 2 cm thick.
Cook burger patties about 2 to 3 minutes on each side, until they are medium roast.
Halve hamburger buns and roast them on the grill until they become mildly dark.
Fill the buns with tzatziki sauce, lettuce, red onion, tomatoes and lamb burger patties.