Heat oil in a large saucepan over medium heat. Whisk in flour until mixture becomes paste-like and light golden, about 1 minute. Gradually whisk in milk until combined; bring to a boil. Cook, stiring continually until mixture thickens, 10 to 15 minutes. Stir in Parmesan cheese and pepper. Remove from heat; set white sauce aside.

Preheat the oven to 375 degrees F (190 degrees C).

Mix mozzarella cheese, spinach, and ricotta cheese together in a medium bowl.

Spread 1/4 cup of the white sauce over the bottom of a rectangular baking dish. Arrange 1/3 of the lasagna noodles over top, overlapping to fit. Spoon 1/2 of cheese-spinach mixture over noodles; top evenly with 1/2 of the salmon. Repeat layers once more. Top with remaining noodles and remaining white sauce. Cover the baking dish with aluminum foil.

Bake in the preheated oven for 40 minutes. Remove foil. Continue baking until bubbly, about 15 minutes more.