In a mixing bowl, combine olive oil, lemon juice, minced garlic, dried oregano, salt, and black pepper.
Add chicken cubes to the bowl and mix well to coat. Marinate for at least 30 minutes.
Preheat the grill to medium-high heat.
Thread the marinated chicken onto skewers.
Grill the chicken skewers for about 10-15 minutes, turning occasionally, until fully cooked.
Warm the pita bread on the grill for a minute or two.
Assemble the gyros by placing grilled chicken, tzatziki sauce, red onion, tomatoes, and lettuce on the pita bread.
Fold and serve immediately.