Season the ground turkey or beef with salt and pepper. Form into 4 patties.
Cook the patties in a skillet over medium heat, or grill them, for about 5-7 minutes on each side or until fully cooked through. The internal temperature should reach 165°F for turkey and 160°F for beef.
While the patties are cooking, prepare the yogurt sauce (if using) by mixing the Greek yogurt, lemon juice, garlic, salt, and pepper in a small bowl. Set aside.
To assemble the wraps, place a lettuce leaf on a plate. On each lettuce leaf, place a cooked burger patty. Top each patty with slices of avocado, tomato, and red onion. Sprinkle shredded cheddar cheese over the top. Add a dollop of mustard, ketchup, or a spoonful of the yogurt sauce if desired.
Carefully fold the lettuce around the fillings to create a wrap. Serve immediately.