In a mixing bowl, combine Greek yogurt, lemon juice, grated cucumber, dill, salt, and pepper. Stir until creamy and refrigerate for 15 minutes.

Heat olive oil in a skillet over medium heat. Sauté minced garlic until fragrant, about 1 minute. Add ground beef and cook until browned, about 5-7 minutes.

Stir in oregano, cumin, paprika, salt, black pepper, and optional cayenne. Cook for another 2-3 minutes.

Warm the pita bread in a dry skillet for 1 minute on each side or in a preheated oven at 350°F for 5 minutes.

Place cooked beef in the center of each pita. Top with red onions, tomatoes, lettuce, and tzatziki. Sprinkle with feta.

Roll the pita around the fillings and serve immediately with extra tzatziki.