01 - Combine Greek yogurt, grated cucumber, minced garlic, dill, lemon juice, olive oil, salt, and pepper in a bowl. Mix thoroughly, cover, and refrigerate until ready to serve.
02 - In a large mixing bowl, combine ground chicken, red onion, garlic, feta, parsley, dill, oregano, cumin, salt, and pepper. Mix gently until just incorporated, being careful not to overwork the meat.
03 - Divide the chicken mixture evenly and shape into 4 uniform patties of equal size.
04 - Heat olive oil in a grill pan or skillet over medium heat. Place patties in the pan and cook for 5-6 minutes per side until golden brown and cooked through, reaching an internal temperature of 165°F.
05 - Lightly toast the burger buns or pita breads until golden and warm.
06 - Place crisp lettuce leaves on the bottom bun, add a cooked chicken patty, spoon generous tzatziki sauce over the top, and layer with tomato and onion slices. Cover with the top bun.
07 - Serve immediately with additional tzatziki sauce on the side for dipping.