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. Keep the bowl handy. Bake for 10 minutes, or until the sweet potatoes are just beginning to soften on the outsides but are still too firm to eat.
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, using a spatula to spread everything into an fairly even layer and stirring it a bit if needed.
Return to 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. (They won’t be browned and caramelized but will be delicious to eat.) Sprinkle with Parmesan. Serve hot.
TO STORE: Leftovers can be stored in an airtight storage container in the refrigerator for up to 4 days.
TO REHEAT: Gently rewarm chicken and vegetables on a lightly greased baking sheet in the oven at 350 degrees F until hot. You can also reheat this dish in the microwave.
TO FREEZE: Store leftovers in an airtight freezer-safe storage container in the freezer for up to 3 months. Let thaw overnight in the refrigerator before reheating. The zucchini and squash may become somewhat mushy and watery once thawed, but the flavors will still be delicious.