Use a mandolin to thinly slice, about an 1/8th inch thick, the zucchini and eggplant into long strips. Line two half sheet trays with paper towel and lay the strips of vegetables over the lined sheet trays. Evenly sprinkle the salt over the vegetables and then top them with another sheet of paper towel. Continue to layer the vegetables and paper towels in single layers until all the vegetables are covered. Let the vegetables stand while you prep the rest of the ingredients, at least 30 minutes; the vegetables will let off their excess moisture.
Meanwhile bring a pot of salted water to a boil. Lay the lasagna noodles on a sheet tray in an even layer. Carefully pour the hot, salted water over the noodles. Let the noodles soak for 20 minutes to soften.
Add 2 tablespoons olive oil to a large sauté pan over medium-high heat. Add the mushrooms and cook about 6-8 minutes or until softened and the excess liquid has evaporated from the pan. Season with salt. Stir in the garlic and cook an additional minute or until fragrant. Next add the spinach to the pan and cook until wilted. Season the mixture again with salt to taste once the spinach has completely wilted and excess liquid has cooked off. Turn the heat off and let the mixture cool.
To a large bowl combine the ricotta, lemon zest, spinach and mushroom mixture, parsley, basil, dried oregano and red pepper flakes. Season the ricotta mixture with salt to taste.
In a 9x13 inch baking dish evenly spread 3/4 cup of tomato sauce over the bottom. Top the sauce with 4 lasagna noodles. Evenly spread one third of the ricotta mixture over the noodles. Next, shingle half of the eggplant slices over the ricotta and press down on the eggplant firmly to ensure the layers are even. Spread another 3/4 cup of sauce over the eggplant followed by half of the zucchini. Again, press down on the zucchini to keep the layers even. Spread another third of the ricotta over the zucchini, followed by four more noodles and another 3/4 cup tomato sauce. Shingle the remaining eggplant over the sauce and press firmly down on the eggplant. Spread the remaining ricotta over the top, the last four noodles and another 3/4 cup tomato sauce. Shingle the zucchini over the top of the lasagna and sprinkle the top with shaved parmesan.
Place the lasagna in the oven and bake for 45 minutes or until the lasagna is bubbling on the sides and the cheese is beginning to brown on top. Remove from the oven and let stand 15 minutes before cutting and serving.