Bring a large pot of water to a boil. Add lasagna noodles and cook according to package directions. Drain and set aside until ready to use.
In a large skillet, heat olive oil on medium-high heat. Add onion and garlic and saute until translucent, about 5 minutes. Add eggplant, season with salt and pepper and saute about 5 minutes until softened. Add mushrooms and cook until vegetables are tender, about 7 minutes. Pour in all but ¾ cup tomato sauce and simmer 5 minutes.
Meanwhile, mix yogurt, egg and Italian seasoning in a bowl and set aside until ready to use.
Preheat oven to 350 degrees. Spray a large casserole dish with olive oil. Spread ¼ cup reserved tomato sauce on the bottom of the dish. Spread a layer of lasagna noodles evenly on the bottom. Top with half the vegetable ‘meat’ sauce. Spread another layer of noodles over the sauce. Top with all of the yogurt sauce. Layer with more noodles and the other half of the tomato sauce. Top with another layer of noodles and half a cup of reserved tomato sauce. Top with mozzarella slices and parmesan cheese.
Bake, covered, for 30 minutes. Remove cover and bake 30 more minutes until bubbly. Set aside to cool before slicing and serving.