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 until softened, about 3 minutes.
Add the flour to the onions and stir for 1 minute until blended.
Whisk in the milk and bring the mixture to a boil, then simmer and stir until the white sauce thickens, about 5 minutes. Remove from heat and season with salt and pepper to taste.
In a mixing bowl, combine the ricotta, squeezed spinach, egg white, and 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 pour another 1 cup of sauce on top.
Top with the remaining 3 noodles and the remaining sauce. Sprinkle grated Parmesan on top if using.
Bake uncovered in the preheated oven until hot and bubbly, about 20 to 25 minutes. Let cool a few minutes before serving.