Place a rack in the center of the oven and preheat the oven to 400 degrees F. For easy cleanup, line a large, rimmed baking sheet with foil. Lightly coat the foil with nonstick spray.
Place the sweet potatoes in a large bowl. Drizzle with 1 tablespoon olive oil and sprinkle with 1/4 teaspoon kosher salt and 1/4 teaspoon black pepper. Toss to coat and then spread into a single layer on the baking sheet. Bake for 10 minutes.
Meanwhile, in the bowl that you used previously for the sweet potatoes, place the chicken, broccoli, bell pepper, zucchini, and yellow squash. Drizzle with the remaining 2 tablespoons olive oil. Add the lemon zest and juice, Italian seasoning, garlic powder, onion powder, and remaining 1 teaspoon salt and 1/2 teaspoon pepper. Toss to coat.
Transfer the chicken and vegetable mixture to the sheet pan with the sweet potatoes. Spread everything into an even layer and stir if needed.
Return the sheet pan to the oven and bake for 15 to 20 additional minutes, stirring once halfway through, until the chicken is cooked through and no longer pink in the middle and the vegetables are tender but not mushy. Sprinkle with Parmesan. Serve hot.