Preheat oven to 350 degrees. Coat a large baking dish with cooking spray. Put a large pot of water on to boil.
Cook noodles in boiling water until not quite al dente, about 2 minutes less than package directions. Drain; return the noodles to the pot, cover with cool water and set aside.
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. Stir spinach into pan; remove from heat.
Mix tomatoes with basil, salt and pepper in a medium bowl.
To assemble lasagna: Spread one-fourth of the tomatoes in prepared baking dish. Arrange a layer of noodles on top, trimming to fit if necessary. Evenly dollop half the cottage cheese over the noodles. Top with half the sausage mixture, one-third of remaining tomatoes and one-third of remaining mozzarella. Continue with another layer of noodles, the remaining cottage cheese, the remaining sausage, half the remaining tomatoes, and half the remaining mozzarella. Top with a third layer of noodles and remaining tomatoes.
Cover the lasagna with foil and bake until bubbling and heated through, 1 hour to 1 hour and 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.