Combine porcini and hot water in a small bowl. Let stand 30 minutes. Drain in a sieve over a bowl, reserving 1/4 cup mushroom liquid. Rinse and drain porcini; finely chop.
Preheat oven to 375°
Heat oil in a large nonstick skillet over medium-high heat. Add onion; sauté 2 minutes. Add the porcini, portobello, shiitake, and button mushrooms. Sprinkle mushrooms with salt; sauté 8 minutes.
Combine the reserved mushroom liquid, wine, tomato paste, rosemary, oregano, and tomatoes in a medium saucepan. Bring to a boil; reduce heat, and simmer 5 minutes.
Combine 1 cup mozzarella, thyme, ricotta cheese, and egg whites in a bowl; set aside.
Arrange 15 polenta slices in the bottom of a 13 x 9-inch baking dish coated with cooking spray. Top with 2 1/2 cups mushroom mixture, 1 cup tomato sauce, and 1 1/4 cups ricotta mixture. Repeat layer with 15 polenta slices, remaining mushroom mixture, 1 cup tomato sauce, and the remaining ricotta mixture. Top with the remaining polenta slices and tomato sauce. Sprinkle the lasagna with 1 cup mozzarella. Cover and bake at 375° for 45 minutes.
Uncover and bake an additional 15 minutes. Let stand 5 minutes.