Preheat oven to 400°. Coat an 8-inch square baking pan with cooking spray. Add 1 cup boiling water to mushrooms; let stand 20 minutes. Drain, reserving liquid. Squeeze dry; roughly chop.
Bring a pot of water to a boil. Add lasagna; cook 9 minutes or until al dente. Place on baking sheet with plastic wrap between layers to prevent sticking.
Bring milk just to a boil in a small saucepan. Meanwhile, melt butter spread in a separate pan over medium heat. Add flour to butter, and cook, whisking constantly, 2–3 minutes or until smooth and bubbling. Slowly add milk, whisking constantly; cook 4–5 minutes or until smooth, thickened, and boiling. Whisk in 1/2 teaspoon salt and nutmeg. Transfer milk mixture (béchamel sauce) to a bowl. Cover, pressing down on surface with plastic wrap; set aside.
Place a large skillet over medium-high heat. When hot, coat with cooking spray. Add zucchini; season with 1/4 teaspoon each salt and pepper. Cook 5 minutes or until lightly browned and just tender. Stir in artichoke hearts, mushrooms and liquid, remaining 1/2 teaspoon salt, and 1/4 teaspoon pepper. Raise heat to high; cook 3–4 minutes or until liquid is absorbed.
Spread 2 tablespoons béchamel over bottom of pan. Cut lasagna to fit without overlapping (about 2 1/2 sheets per layer). Spread one-quarter of sauce over noodles. Scatter one-third spinach and one-third vegetables on top. Dollop with one-third ricotta; sprinkle with 1 tablespoon Parmesan. Top with a layer of noodles; repeat 2 more times. Finish with noodles, and top with remaining béchamel; sprinkle with remaining Parmesan. Cover with foil; bake 25 minutes. Remove foil; bake 25 minutes or until top is golden. Remove from oven; let stand 20 minutes.