Preheat the oven to 400°F (200°C).
Heat the olive oil in a nonstick saucepan over medium-high heat. Add the finely chopped onion and cook, stirring, until softened, about 3 minutes.
Stir in the flour and cook 1 minute to remove the raw taste.
Whisk in the milk and bring the mixture to a boil, then reduce heat and simmer until the white sauce thickens, about 5 minutes. Remove from heat and season with salt and pepper to taste.
In a bowl, combine the ricotta, squeezed dry chopped spinach, egg white, and ground nutmeg until evenly mixed.
Spoon 1 cup of the white sauce into the bottom of an 11×7-inch baking dish.
Arrange 3 no-boil lasagna noodles over the sauce. Spread half of the ricotta–spinach mixture evenly over the noodles, then top with 1 cup of sauce.
Layer 3 more noodles, spread the remaining ricotta mixture over them, and top with another 1 cup of sauce.
Top with the remaining 3 noodles and the rest of the white sauce. Sprinkle grated Parmesan over the top if using.
Bake uncovered until hot and bubbly and heated through, about 20 to 25 minutes. Let rest a few minutes before serving.
