Line a fine mesh strainer with two layers of cheesecloth and place yogurt in it over a large bowl.

Cover and refrigerate for at least 4 hours or overnight to drain the yogurt.

Drain and discard the liquid from the yogurt, setting the thickened yogurt aside.

Place chopped cucumber in a colander over another bowl and sprinkle with salt.

Let the cucumber stand for 15 minutes to drain liquid.

Discard the liquid from the cucumber.

In a large bowl, whisk olive oil and white vinegar until blended.

Stir in minced garlic, the reserved thickened yogurt, and drained cucumber.

Cover and refrigerate the cucumber sauce until serving.

In a large bowl, combine plain yogurt, minced garlic, crushed dried rosemary, lemon-pepper seasoning, and salt.

Crumble ground lamb or pork over the yogurt mixture and mix well.

Shape the meat mixture into four oval patties.

Preheat grill to medium heat.

Grill patties, covered, over medium heat for 6-7 minutes on each side, or until a thermometer reads 160°F.

Serve gyro burgers in halved pita bread with sliced cucumber and cucumber sauce.