Marinate the Chicken:
In a bowl, mix the garlic, lemon juice, olive oil, oregano, salt, and pepper. Add the chicken and ensure it's fully coated. Marinate for at least 30 minutes, preferably a few hours in the fridge.
Prepare the Tzatziki Sauce:
Combine the Greek yogurt, grated cucumber, minced garlic, olive oil, and dill in a bowl. Season with salt and pepper to taste. Chill until ready to use.
Cook the Chicken:
Heat a grill or skillet over medium-high heat. Remove the chicken from the marinade and cook for about 5 minutes on each side or until the chicken is golden brown and cooked through.
Assemble the Gyros:
Warm the pita breads on the grill or in a dry skillet. Slice the cooked chicken into strips.
Spread tzatziki sauce on each pita, add chicken, and top with onions, tomatoes, and lettuce. Roll up the pita around the fillings.