In a medium bowl, combine Greek yogurt, lemon juice, grated cucumber, chopped dill, salt, and pepper. Stir until well blended, then cover and chill in the refrigerator for at least 15 minutes.

Heat olive oil in a large skillet over medium heat. Add minced garlic and sauté for about 30 seconds until fragrant.

Increase the heat slightly and add ground beef, cooking for 5-7 minutes until browned. Stir occasionally to break it apart.

Once the beef is cooked, stir in oregano, cumin, paprika, salt, black pepper, and cayenne pepper. Cook for an additional 2-3 minutes.

While the beef finishes, heat pita bread in a skillet or oven until warm and pliable.

Assemble gyros by spooning beef mixture into warmed pita, layering with red onion, tomato, lettuce, and a dollop of tzatziki.