Bring the tomato sauce to a boil, stir in the zucchini, and cook for about 5 minutes.
Ladle a bit of sauce into the baking dish and spread it around so that the bottom of the dish is lightly coated.
Preheat oven to 350.
Place lasagne noodles in the pan to form a single layer. If necessary, break noodles to fill gaps.
Spread 1/3 of the ricotta cheese on the noodles and place them in the dish, then top with 1/3 of the spinach and 1/3 of the mozzarella. Generously cover with tomato sauce.
Repeat twice, using 1/3 of ingredients for each layer, saving a bit of cheese to garnish the top.
Bake for about an hour, until sauce is bubbly and cheese is melted. Let cool slightly and serve.