Mix 0.5 cup Greek yogurt, 2 tbsp lemon juice, 2 tbsp olive oil, 2 minced garlic cloves, and 1 tbsp dried oregano in a bowl. Add the 1.5 lbs of chicken and marinate for at least 30 minutes.
Preheat a grill or skillet over medium-high heat. Cook the marinated chicken for 6 to 8 minutes per side until the internal temperature reaches 165F. Let rest, then slice thinly.
Make the tzatziki sauce by combining the remaining 0.5 cup Greek yogurt, 0.5 cup grated cucumber, 2 remaining minced garlic cloves, 1 tbsp lemon juice, and 1 tbsp fresh dill. Season with salt and pepper.
Warm the 4 pita flatbreads on the grill or skillet for 30 seconds per side.
Assemble the wraps by spreading tzatziki sauce on each flatbread, adding sliced chicken, 1 cup lettuce, 0.5 cup red onion, and 1 cup diced tomatoes. Fold and serve immediately.