Prepare marinade by whisking together olive oil, lemon juice, oregano, thyme and garlic in a glass dish. Add cubed pork and marinate for 6 hours in refrigerator or overnight.
Meanwhile, prepare tzatziki by combining yogurt, cucumber, garlic, lemon juice, dill, salt and pepper. Chill at least 1 hour to blend the flavours.
Thread the pork onto metal skewers or bamboo skewers that have been soaked in water for 30 minutes.
Preheat barbecue on HIGH and brush grids with vegetable oil to prevent sticking. Reduce the heat to MEDIUM, and place the pork skewers on the grill. Cook 4 – 6 minutes per side, turning once.
Lightly grill each side of the pita bread, place the pork inside the pocket, and serve with tzatziki sauce.