Preheat oven to 375°F (190°C).
In a large skillet, heat olive oil over medium-high heat. Sauté shrimp and garlic until shrimp turn pink, approximately 3 minutes. Remove from heat and set aside.
In a medium saucepan, melt butter over medium heat. Whisk in flour and cook for 1 minute. Gradually whisk in milk until thickened. Season with salt, pepper, and nutmeg to create a bechamel sauce.
In a small bowl, combine ricotta cheese and egg until smooth.
Spread a thin layer of bechamel sauce in the bottom of a 9x13 inch baking dish.
Layer lasagna noodles, ricotta mixture, spinach, shrimp, bechamel sauce, and mozzarella cheese.
Repeat layers, finishing with a layer of noodles topped with remaining bechamel, mozzarella, and Parmesan cheese.
Cover with foil and bake for 25 minutes. Remove foil and bake for an additional 15-20 minutes until bubbly and golden brown.
Allow the lasagna to rest for 10-15 minutes before slicing.