In a medium bowl, combine Greek yogurt, lemon juice, and grated cucumber. Add dill, season with salt and pepper, mix well, and refrigerate for at least 15 minutes.

Heat olive oil in a large skillet. Add garlic and sauté for about 30 seconds. Then add ground beef, breaking it apart, and cook until browned, about 5 to 7 minutes.

Once the beef is browned, sprinkle in oregano, cumin, paprika, and season with salt and pepper. Optional: add cayenne pepper to taste. Cook for an additional 2 to 3 minutes.

Warm pita bread in a skillet or oven. Keep them warm and soft for assembly.

To assemble, place seasoned beef in the center of a warm pita. Top with red onion, tomato, lettuce, and tzatziki sauce.

Sprinkle crumbled feta cheese on top, roll the pita tightly, and serve immediately with extra tzatziki for dipping.