In a small bowl, stir together the mayonnaise, Italian dressing, feta cheese and anchovies. Season with cayenne pepper, black pepper and salt. Mix until well blended, then set aside.
Heat oil in a large frypan over medium-high heat. Place the tilapia fillets in the frypan, and season with lemon pepper, salt and cayenne. Fry until browned on each side and fish flakes easily with a fork, 5 to 7 minutes.
Warm pita breads in the toaster or in the microwave to soften. Open from the cut side to make pockets. Fill pita bread halves with lettuce, onion and tilapia fillets, then spoon in some of the feta cheese sauce.