Heat the oil in a nonstick saucepan over medium-high heat. Add the onion and cook until slightly wilted, about 3 minutes. Add the flour, stirring until blended. Whisk in the milk and bring to a boil. Boil until the white sauce thickens, about 5 minutes. Remove from the heat. Add salt and pepper, to taste.
Meanwhile, combine the ricotta cheese, spinach, egg white and nutmeg in a bowl. Spoon 1 cup of the sauce onto the bottom of an 11x7-inch baking dish. Arrange 3 noodles over the sauce. Spread ½ of the ricotta mixture evenly over the noodles. Top with 1 cup sauce. Layer 3 more noodles, the remaining ricotta mixture, and 1 cup sauce. Top with the remaining noodles and sauce. Bake, uncovered, until hot and bubbly, 20 to 25 minutes.
Notes
If you want a cheesy element to this lasagna, add shredded mozzarella and Parmesan between layers and on top. Note that the nutritional information will change with added cheeses.