To make the spinach: In a large skillet heat olive oil or butter over medium heat. Add spinach and cook for 2 minutes until wilted. Remove from the heat, drain well, and set aside to cool. Once cooled, Squeeze out the excess moisture.
To make the tomato sauce: In a large skillet, melt butter over medium heat. Add onion and cook for a few minutes, stirring occasionally, until soft and translucent. Add garlic and cook until fragrant, 1-2 minutes. Add crushed tomatoes and sugar, and season with salt and pepper. Bring just to a boil, then remove from heat. Let cool completely.
Preheat the oven to 350°F/175°C.
Assemble the lasagna: Place 3 lasagne noodles (or enough to cover the surface) at the bottom of a 9x13 inch (20x30 cm) baking dish. Spread 1/3 of the tomato sauce, then top with 1/3 of the spinach, 1/3 of the ricotta cheese, and 1/3 of the mozzarella cheese. Repeat with a second layer of noodles, tomato sauce, spinach, ricotta, and mozzarella, then repeat one more time with a third layer.
Place into oven and bake for 35-45 minutes, until golden and bubbling. Let cool for 10-15 minutes before serving, so that the lasagna noodles can soak up all the extra moisture.
Top with chopped fresh parsley or basil leaves if you like.