Preheat the oven to 350°. In a large skillet, heat 1/4 cup olive oil over high heat. Add the mushrooms, season with salt and pepper and cook until softened, about 3 minutes. Transfer to a medium bowl. Add the tomatoes to the skillet, scraping up any browned bits from the bottom of the pan, and cook until softened, 6 to 7 minutes.
Using a food processor, process the toasted almonds, parmesan, garlic, lemon peel, lemon juice and remaining 1/2 cup olive oil into a coarse paste. Transfer the pesto to a bowl and season to taste with salt and pepper.
In an 8-inch square baking dish, spread half the tomatoes across the bottom. Place 2 lasagna sheets on top. Spread a third of the pesto over the sheets; sprinkle with half the mozzarella and then half the mushrooms. Add another layer of lasagna sheets, pesto, mozzarella and mushrooms. Top with another layer of lasagna sheets, spread with the remaining pesto and then the remaining tomatoes. Cover tightly with foil and bake for 35 minutes. Uncover and bake for 10 minutes more. Let stand for at least 10 minutes before slicing.