In a large bowl, combine minced garlic, ground cumin, ground coriander, ground paprika, olive oil, salt, and black pepper. Rub this mixture all over the lamb shoulder and let it marinate for at least 1 hour, preferably overnight in the refrigerator.

Cook the Lamb

Preheat your oven to 160°C (320°F). Place the marinated lamb in a roasting pan. Roast for about 2 to 2.5 hours or until the lamb is tender and easily pulls apart with a fork. Let it rest for 15 minutes before slicing thinly.

Make the Tzatziki Sauce

In a bowl, mix together Greek yogurt, diced cucumber, lemon juice, chopped dill, salt, and pepper to taste. Adjust seasoning as needed.

Assemble the Gyros

Warm the pita bread in a skillet or microwave. Place a generous amount of sliced lamb on each pita, then top with diced tomatoes, red onion, fresh parsley, and tzatziki sauce. Wrap the pita around the filling and serve immediately.