Slice the beef into thin strips. In a bowl, combine with olive oil, lemon juice, minced garlic, salt, pepper, and the spice blend. Let it marinate for at least 1 hour.
Heat a skillet over medium heat. Cook the beef for 8-10 minutes, until browned on all sides and cooked through.
Meanwhile, prepare the tzatziki sauce: grate the cucumber, squeeze out the excess liquid, then mix with Greek yogurt, finely chopped garlic, dill, salt, and pepper.
Slice the tomatoes and red onion into thin rounds.
Warm the pita bread in a skillet or oven until slightly crisp.
Fill the warm pitas with the cooked beef, then top with fresh tomatoes, red onion, and a generous dollop of tzatziki sauce.
Fold the pita and serve immediately, optionally drizzled with olive oil.
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