In a bowl, combine the minced garlic, dried oregano, ground cumin, ground coriander, paprika, ground cinnamon, ground allspice, lemon juice, olive oil, salt, and pepper.
Add the thinly sliced meat to the marinade and mix well to coat. Cover and refrigerate for at least 1 hour, preferably overnight.
In a bowl, combine the Greek yogurt, grated and drained cucumber, minced garlic, olive oil, lemon juice, chopped dill, salt, and pepper.
Mix well and refrigerate until ready to use.
Heat a large skillet or grill pan over medium-high heat.
Add the marinated meat and cook until browned and cooked through, about 5-7 minutes.
While the meat is cooking, warm the pita breads in a dry skillet or in the oven until soft and pliable.
Place a warm pita bread on a plate.
Add a generous amount of cooked meat in the center of the pita.
Top with sliced tomato, sliced red onion, lettuce leaves, and a spoonful of tzatziki sauce.
Sprinkle with crumbled feta cheese if desired.
Enjoy your meal!