Begin by cleaning and deveining the shrimp, then cut them into bite-sized pieces. Halve large scallops to ensure uniformity with the shrimp and pat crab meat dry.

In a medium saucepan over medium heat, melt 4 tablespoons of butter until bubbly. Whisk in 1/4 cup of flour for about 2 minutes. Gradually add 2 cups of milk while whisking until thickened. Season with salt and pepper.

In a large mixing bowl, combine the seafood: prepared shrimp, scallops, and crab meat. Fold in 1 cup of shredded mozzarella and 1/2 cup of grated Parmesan, reserving some cheese for the top layer.

Preheat the oven to 375°F (190°C). In a greased baking dish, layer lasagna noodles, a portion of the seafood mixture, and béchamel sauce. Repeat layers, finishing with noodles and béchamel topped with reserved cheese.

Cover the lasagna with foil and bake for 25 minutes. Remove the foil to crisp the top and bake for an additional 15-20 minutes until golden.

For a crispy top, broil for the last 2 minutes, keeping a close watch to avoid burning.

Let the lasagna sit for 15 minutes before slicing to allow layers to set.