Marinate the chicken. Whisk olive oil, garlic, paprika, cumin, oregano, onion powder, cayenne, salt, pepper, and lemon juice together. Add chicken thighs and toss to coat. Marinate at least 30 minutes, or up to overnight in the fridge.
Make the tzatziki. Combine Greek yogurt, squeezed cucumber, garlic, dill, lemon juice, olive oil, and salt. Stir well and refrigerate until ready to use. (The longer it sits, the better the flavor.)
Cook the chicken. Heat a grill pan or skillet over medium-high heat. Cook marinated chicken 6–7 minutes per side until deeply charred and cooked through (internal temp 165°F / 74°C). Let rest 5 minutes, then slice into strips.
Warm the pitas. Lightly brush pitas with olive oil. Toast in a dry skillet or grill pan 1 minute per side until warm and slightly charred.
Assemble the gyros. Spread a generous layer of tzatziki on each pita. Layer lettuce, sliced chicken, tomatoes, red onion, and crumbled feta. Drizzle with extra tzatziki and fold or wrap.
Serve immediately while warm and crisp.