In a large bowl, combine the ground lamb and ground beef with the red wine vinegar, minced garlic, onion powder, oregano, crushed rosemary, salt, pepper, and lemon zest. Mix gently with your hands until just combined—don't overwork the meat or it will become tough and dense. While the meat chills, prepare your mise en place: thinly slice the red onion into rings, cut the tomatoes into ¼-inch rounds, chop the fresh parsley, and arrange the lettuce on a serving platter. Having everything ready before you start cooking will keep the assembly process smooth and fast.

Cover the meat mixture and refrigerate for 30–60 minutes to let the flavors meld and the meat firm up, making it easier to shape and sear. Remove from the refrigerator about 15 minutes before cooking and let it rest at room temperature—this allows the meat to cook more evenly when it hits the hot grill.

Divide the meat mixture into 6 equal portions and gently shape each into a loose ball—don't compress them too much. Preheat your grill to medium-high heat (around 400°F) and lightly oil the grates to prevent sticking. I recommend having the pitas nearby and ready to use, as you'll be moving quickly once the meat hits the grill.

Place a meat ball directly on the hot grill, then immediately top it with a pita bread and press down firmly with a grill press or the back of a sturdy spatula, smashing the meat into a thin patty that adheres to the pita. Cook for 3 minutes without moving—this creates a flavorful, browned crust on the meat side. Flip the burger (the pita will now be on top facing up) and cook for another 2 minutes on the second side until the pita is warm and lightly charred and the meat is cooked through. Repeat with the remaining 5 meat balls and pitas.

Arrange each cooked burger (pita-side up) on the lettuce-lined platter or on individual plates. Spread or drizzle the tzatziki sauce over the warm meat, then layer with the sliced tomatoes, red onion rings, and chopped fresh parsley. Serve immediately while the pita is still warm and the flavors are at their peak.