1. Preheat oven to 350 degrees F. Coat a 9-by-13-inch glass baking dish with cooking spray. Put a large pot of water on to boil.
2. Cook noodles in the boiling water until not quite al dente, about 2 minutes less than the package directions. Drain; return the noodles to the pot, cover with cool water and set aside.
3. Coat a large nonstick skillet with cooking spray and heat over medium-high heat. Add sausage and cook, crumbling with a wooden spoon, until browned, about 4 minutes. Add mushrooms and water; cook, stirring occasionally and crumbling the sausage more, until the sausage is cooked through, the water has evaporated and the mushrooms are tender, 8 to 10 minutes. Squeeze spinach to remove excess water, then stir into the pan; remove from heat.
4. Mix tomatoes with basil, salt and pepper in a medium bowl.
5. To assemble lasagna: Spread 1/2 cup of the tomatoes in the prepared baking dish. Arrange a layer of noodles on top, trimming to fit if necessary. Evenly dollop half the ricotta over the noodles. Top with half the sausage mixture, one-third of the remaining tomatoes and one-third of the mozzarella. Continue with another layer of noodles, the remaining ricotta, the remaining sausage, half the remaining tomatoes and half the remaining mozzarella. Top with a third layer of noodles and the remaining tomatoes.
6. Cover the lasagna with foil and bake until bubbling and heated through, 1 hour to 1 hour 10 minutes. Remove the foil and sprinkle the remaining mozzarella on the lasagna. Return to the oven and bake until the cheese is just melted but not browned, 8 to 10 minutes. Let rest for 10 minutes before serving.