In a medium bowl, stir together all ingredients for the cucumber tomato salsa. Set aside in the refrigerator until ready to use.
Grate the English cucumber into a small bowl for the tzatziki sauce. Stir in remaining ingredients for the sauce until well-combined and smooth.
Warm the pita in a cast iron skillet or griddle pan over medium heat for about 10 to 20 seconds per side until softened.
Warm the leftover lamb in the microwave.
To assemble, spread about 1 to 2 Tbsp in the center of each pita. Divide the lamb evenly between the pitas. Top with cucumber tomato salsa, feta crumbles, and fresh parsley.