PREHEAT grill to medium-high heat and brush grates with oil.
CHOP half the cucumber and slice the remaining half into rounds.
COMBINE chopped cucumber, yogurt, dill, garlic and vinegar in a medium bowl. Season with salt and pepper.
GRILL sausages until exterior is crisp and char marks appear, about 5 to 6 minutes per side.
SLICE sausage into 1-inch thick rounds.
SPREAD yogurt sauce inside pita halves and fill with lettuce, tomato, onion, sliced cucumber and cooked sausage. Repeat with remaining pitas and serve.