Preheat the oven to 450ºF. Coat a 9x13 inch baking pan with cooking spray.
Cut the zucchini in half lengthwise, then into ½ inch slices. Peel and halve the onions, then cut into 1 inch chunks. Place the vegetables in a single layer on a baking sheet, using two if necessary to achieve a single layer. Drizzle with oil and season with salt and pepper. Toss to coat. Roast the vegetables for 15 minutes. Toss and continue to roast, about 20 minutes more or until brown and soft. Remove from the oven and reduce the oven temperature to 375ºF.
Bring a large pot of water to boil and cook lasagna according to package directions. Drain the pasta in a colander and run under cold water until cool enough to handle. Separate the pasta and blot it dry with a kitchen towel.
In a medium bowl, mix ricotta, eggs, ½ cup of the Parmesan, and salt and pepper to taste until well combined.
Spread a thin layer of sauce in the bottom of the prepared pan. Cover with a layer of pasta, slightly overlapping the noodles. Spread with one-third of the ricotta mixture. Sprinkle one-quarter of the mozzarella and one-quarter of the remaining ½ cup Parmesan over the ricotta. Spoon one-third of the roasted vegetables on top and then ½ cup sauce. Add another layer of pasta and continue layering until you have 4 layers of pasta and 3 layers of filling. Spread the remaining sauce on top and sprinkle with the remaining mozzarella and Parmesan.
Cover the pan with aluminum foil and bake for 30 minutes. Uncover and continue to bake until golden and bubbly, about 15 minutes more. Let stand for 15 minutes before serving.