Preheat grill or cast iron griddle pan. If using a griddle pan, set heat to medium-low. Grill each side of the chicken for 5-6 minutes. Once the chicken is finished, lower the griddle temperature to low and warm each side of the pita, about 2 minutes per side. While warming the pitas, allow the chicken to rest for about 5 minutes before thinly slicing. Assemble pitas by layering tzatziki, chicken, and lettuce.