In a medium bowl, add the mayonnaise, Dijon mustard, red wine vinegar, dried dill, and a pinch of salt and black pepper, and whisk until well combined.
To the same bowl, add the lettuce, tuna, tomatoes, celery, red onion, and parsley, and then – using tongs or your hands – toss until well coated in the dressing. Taste and adjust seasoning with salt and pepper to taste.
Optional: If you prefer a warm pita, you can warm your pita in an oven at 350°F for a few minutes or in the microwave for 15-30 seconds.
Place the pita on a cutting board and slice it in half, then use your hands to open each side to create a pocket. Then fill each side of the pocket with the tuna salad mixture.