Preheat the oven to 375 degrees F. Spray a 13 by 10-inch aluminum foil pan with vegetable oil cooking spray.
In a large pot of boiling salted water, cook the lasagna noodles until they are just done, about 8 minutes. Drain and set aside.
Melt the butter in a large, heavy skillet and cook the onion over low heat until very soft, about 5 minutes. Add the garlic and cook about 1 minute more. Over medium-low heat, stir in the flour with a whisk, then gradually add the half-and-half, allowing the sauce to thicken slightly before adding more. When the sauce has thickened to about the consistency of whipping cream, add the cheese and stir well. Add the salt and pepper and stir again. Add the scallops and cook for about 3 to 4 minutes, then add the shrimp and cook for 1 to 2 minutes or just until the shrimp turn pink. Turn off the heat.
Spoon about 2 tablespoons of the sauce from the skillet into the prepared pan. Cover the bottom of the pan with 4 noodles, placing them side by side. Spoon 1/3 of the sauce over the noodles, distributing half of the seafood evenly. Layer 4 more noodles, 1/3 of the sauce, and remaining seafood. Cover with the last 4 noodles and the remaining sauce. (For the top layer, do not spoon any seafood on top of the noodles; just use the sauce.) Tuck in any edges of the noodles so they're all coated with sauce. Top with the Parmesan.
Bake for 20 to 25 minutes, uncovered, until bubbly. Allow to sit for 10 minutes before slicing.