Preheat the oven to 375°F and spray a 9 x 13 x 2 1/2-inch baking dish with nonstick spray; set aside.
Heat the olive oil in a large skillet over medium-high heat.
Add the diced zucchini, chopped mushrooms, diced carrots, and diced onion to the skillet and cook 4–5 minutes until the vegetables are tender.
Add the spinach and cook 1 minute more, until it wilts.
Stir in the crushed tomatoes, tomato sauce, tomato paste, Italian seasoning, sugar, and chopped basil. Reduce heat to low and simmer about 10 minutes, then season with salt and ground black pepper to taste.
Meanwhile, bring a large pot of water to a rolling boil and cook the lasagna noodles 8 minutes or until al dente; drain and rinse with cold water to stop cooking.
In a medium bowl, combine the ricotta, grated Parmesan, and the egg until smooth.
Assemble the lasagna: spread 1 cup of the vegetable tomato mixture over the bottom of the prepared dish. Place a single layer of noodles on top, spread 1/2 cup of the ricotta mixture over the noodles, and sprinkle with a handful of shredded mozzarella. Repeat layers until ingredients are used, finishing with the remaining mozzarella on top.
Cover the dish with aluminum foil and bake 20 minutes. Remove the foil and bake an additional 20–25 minutes until heated through and the top is bubbly and browned.
Let the lasagna cool 10 minutes before slicing and serving.