Preheat oven to 375°F. Cook lasagne noodles according to package directions, drain, and lay flat on a baking sheet to prevent sticking.
Heat olive oil in a large skillet over medium heat. Add onion and cook for 5 minutes until softened. Add garlic, zucchini, and mushrooms, and cook for 8-10 minutes until vegetables are tender and liquid has evaporated. Stir in spinach and cook until wilted. Season with salt and pepper.
In a medium bowl, combine ricotta cheese, egg, 1 cup mozzarella, 1/2 cup Parmesan, nutmeg, and Italian seasoning. Mix well.
Spread 1 cup of marinara sauce on the bottom of a 9x13 inch baking dish. Layer 4 lasagne noodles over the sauce.
Spread half of the ricotta mixture over the noodles, then top with half of the vegetable mixture and 1/2 cup marinara sauce. Sprinkle with 1/2 cup mozzarella.
Repeat layers: 4 noodles, remaining ricotta mixture, remaining vegetables, 1/2 cup marinara sauce, and 1/2 cup mozzarella.
Top with final 4 noodles, remaining marinara sauce, remaining 1 cup mozzarella, and remaining 1/2 cup Parmesan.
Cover with foil and bake for 30 minutes. Remove foil and bake an additional 15 minutes until cheese is bubbly and golden. Let rest for 10 minutes before slicing.