In a large bowl, combine the ground lamb or beef with ground cumin, coriander, smoked paprika, garlic powder, onion powder, salt, and black pepper. Mix well until the spices are evenly distributed.
Heat a large skillet over medium-high heat. Add the meat mixture and cook, breaking it up with a spoon, until browned and cooked through, about 10-15 minutes.
Warm the pita breads in a dry skillet or microwave. Divide the cooked meat among the pitas and top with sliced onions, diced tomatoes, and tzatziki sauce.
Serve immediately and enjoy your Easy Doner Style Gyros.