In a bowl, combine the ground lamb with minced garlic, fresh mint, fresh parsley, ground zira, ground coriander, ground black pepper, and salt. Mix until just combined.
In another bowl, stir together the Greek yogurt, diced cucumber, chopped pistachios, chopped cilantro, salt, and red pepper. Cover and refrigerate.
Form the lamb mixture into 5 equal patties.
Preheat grill to 175-200°C (347-392°F).
Spray the grill grate with non-stick cooking spray.
Grill the patties for 7-8 minutes on each side until the internal temperature reaches 63°C (145°F).
Place a grilled lamb patty on each pita bread with yogurt sauce. Garnish with cucumber slices, pistachios, and fresh mint leaves.