In a large mixing bowl, combine the ground lamb and ground beef.
Add the finely chopped onion, minced garlic, dried oregano, ground cumin, paprika, cinnamon, ground coriander, cayenne pepper, red wine vinegar, olive oil, salt, and pepper.
Mix the ingredients thoroughly until well combined.
Preheat the Blackstone griddle to medium-high heat.
Place the meat mixture onto the hot griddle and shape it into long, thin patties.
Cook the patties for 6-7 minutes on each side, or until they are well-browned and cooked through.
While the meat is cooking, warm the pita bread on the griddle for about 30 seconds on each side until they are soft and pliable.
Once the meat is cooked, remove the patties from the griddle and let them rest for a couple of minutes. Slice the patties into thin strips.
Stir together the tzatziki sauce ingredients together in a small bowl.
Assemble the gyros by placing a few slices of the cooked meat on each pita bread. Top with sliced tomatoes, onions, lettuce, and a generous dollop of our the tzatziki sauce.
Fold the pita bread around the fillings and serve the gyros immediately. Enjoy!