Preheat a grill on medium heat to 400 degrees F. Alternatively, preheat a two-burner grill pan over medium-high heat. Clean and oil the grill grates or grill pan.
Meanwhile, make the sauce: In a small food processor, combine the lemon zest and juice, tahini, garlic, water, olive oil, maple syrup, cumin, turmeric, 1 teaspoon salt and 1/4 teaspoon pepper. Process until smooth. Taste for seasoning. Set aside.
Drizzle both sides of the eggplant, yellow squash and zucchini with olive oil and sprinkle with salt and pepper. Grill each side until tender and charred, 3 to 4 minutes. Remove and let cool slightly, then cut into 1/2-inch cubes. Transfer to a large bowl; add the chickpeas, chopped dill, sesame seeds and a sprinkle of salt and pepper. Toss together.
When ready to serve, lightly grill both sides of each pita. Gently fold the pitas in half, keeping them intact, and fill with the vegetable mixture. Top each pita with 1 to 2 cucumber ribbons, a liberal drizzle of the sauce and a few dill fronds and oregano leaves. Serve warm or at room temperature.