Combine the steak, onion, pumpkin pie spice, 2 tablespoons lemon juice, 1 tablespoon olive oil, 1 minced garlic clove, 2 tablespoons chopped herbs, 1 teaspoon salt and 1/2 teaspoon pepper in a bowl; toss well to coat. Set aside while you prepare the salad.
Whisk the tahini, the remaining garlic and 2 tablespoons lemon juice, and 1 tablespoon olive oil in a separate bowl; stir in the tomatoes and cucumbers.
Heat a cast-iron skillet over medium-high heat until very hot. Brush the pitas with the remaining 1 tablespoon olive oil; cook until lightly toasted, about 1 minute per side. Transfer to plates. Working in batches, add the meat and onion to the skillet in a single layer and cook until browned, about 2 minutes per side. Serve the steak and onion on the pitas with the cucumber salad. Top with the remaining herbs.