Heat oil in a large skillet over medium heat. Add onion; cook 10 minutes or until onion is browned, stirring occasionally. Stir in garlic and spinach. Reduce heat, cover, and cook 3 minutes or until spinach is tender. Set aside.
Lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, milk, salt, black pepper, and red pepper in a small saucepan, stirring with a whisk. Bring to a boil over medium-high heat, stirring frequently. Reduce heat and simmer 1 minute, stirring frequently. Add 2 cups milk mixture to spinach mixture. Cover remaining milk mixture, and set aside.
Spread 1/2 cup marinara sauce in bottom of a 13 x 9-inch baking dish coated with cooking spray. Arrange 3 lasagna noodles over sauce; top with half of spinach mixture. Top with 3 lasagna noodles, 1 cup marinara sauce, and 3/4 cup cheese. Layer 3 more lasagna noodles, remaining spinach mixture, and remaining 3 lasagna noodles. Top with remaining marinara sauce. Pour reserved milk mixture over the top, and sprinkle with remaining 3/4 cup cheese. Bake at 375° for 50 minutes or until lasagna is browned on top. Garnish with parsley sprigs, if desired.