Preheat oven to 400 degrees F (200 degrees C). Spray a large baking sheet with cooking spray.
Arrange zucchini, bell peppers, mushrooms, and onion wedges on prepared baking sheet. Scatter basil and garlic over vegetables and spray with cooking spray. Season with salt and black pepper.
Bake in preheated oven until vegetables are lightly browned and tender, 10 to 25 minutes.
Bring a large pot of lightly salted water to a boil. Cook lasagna in the boiling water, stirring occasionally until cooked through but firm to the bite, about 8 minutes. Drain.
Bring pasta sauce to a simmer in a saucepan over medium-high heat. Mix mozzarella cheese and Parmesan cheese in a bowl.
Pour about 1/3 cup pasta sauce in a 9x13-inch baking dish. Layer 3 lasagna noodles over sauce. Spread about of 1/4 the roasted vegetables over noodles and top with about 1/4 the sauce. Sprinkle 1/4 of the mozzarella-Parmesan cheese mixture over the sauce. Repeat layers 3 more times, ending with the cheese.
Bake in preheated oven until cheese is melted and sauce is bubbly, 20 to 25 minutes. Allow lasagna to rest for 10 minutes before slicing.