Preheat the oven to 375 degrees . In a small saucepan, melt the butter over medium-low heat. Whisk in the flour until smooth. Slowly add the milk and cook, whisking continuously, until thickened, about 8 minutes. Season the cream sauce with salt and nutmeg.
Coat the bottom of a 9-by-13-inch baking dish with 1 cup tomato puree and cover with 4 lasagna sheets. Layer the lasagna as follows: tomato puree, basil, zucchini, mozzarella, ricotta, cream sauce, Parmesan and lasagna sheets. Repeat the layering, gently pressing down each layer. Finish with a layer each of tomato puree, basil, zucchini and cream sauce. Top with the Parmesan. Bake until golden and bubbly, about 30 minutes. Let sit for about 5 minutes before cutting into squares.