Put the squash in a large microwave-safe bowl. Add 1 tablespoon dill, a splash of water, and salt and pepper to taste. Cover with plastic wrap, pierce the plastic and microwave until tender, 15 minutes.
Meanwhile, heat 1 tablespoon olive oil in a large nonstick skillet over medium-high heat. Add the onion and garlic; cook, stirring, until soft, 3 minutes. Stir in the tofu and 1/4 teaspoon salt; cook, undisturbed, 2 minutes, then cook, stirring, until browned, 3 more minutes.
Push the tofu and onion to one side of the pan; add half of the tomatoes to the other side and season with salt. Cook, stirring the tomatoes, 3 minutes, then stir into the tofu and onion mixture. Add half of the spinach and a splash of water and stir until the spinach wilts. Stir in 1 tablespoon parmesan and 1 teaspoon lemon juice.
Toss the pitas, the remaining spinach, tomatoes, 3 tablespoons dill, 1 tablespoon parmesan, 2 tablespoons olive oil, 2 teaspoons lemon juice, and salt to taste in a bowl. Spoon the tofu mixture into the squash. Serve with the salad.