Mix all of the ingredients for the sauce into a bowl. Season with salt and pepper to taste. Adjust any of the ingredients as needed to taste. Set aside.
Heat a nonstick pan over medium heat. Once hot, add the oil. Crumble in the ground chicken, lemon pepper seasoning, salt and pepper. Brown well while breaking it up into smaller pieces until it is no longer pink. Mix the feta into the chicken until fully combined then remove from the heat.
Warm the pita on both sides in a pan over medium heat for approximately 30 seconds per side.
Layer the pita with lettuce, ground chicken, tomato, onion, sauce, and cucumber. Fold in half and serve with chips and dolmas.