Arrange a rack in the middle of the oven and heat the oven to 350°F.

Melt 4 tablespoons unsalted butter in a medium saucepan over medium heat. Add ¼ cup all-purpose flour and cook, stirring, until very lightly toasted, about 2 minutes. Slowly pour in 1 (8-ounce) bottle clam juice and then 3 cups whole milk while whisking. Season with 1 ½ teaspoons kosher salt and ¼ teaspoon black pepper. Bring to a boil, stirring frequently. Reduce heat to medium and simmer until thickened, 8 to 10 minutes more. Taste and season with more kosher salt and black pepper as needed.

Meanwhile, cook 1 pound dried lasagna noodles in salted boiling water according to package directions until al dente. Drain, rinse under cool water until cool, and drain well again. Arrange the noodles in an even layer on a large baking sheet, coating them with olive oil.

Pick the leaves from ½ bunch fresh parsley and finely chop until you have ¼ cup for the sauce and 1 tablespoon more for garnish. Juice ½ medium lemon until you have 1 tablespoon juice. Finely chop 4 garlic cloves.

Melt 4 tablespoons unsalted butter in a large skillet over medium heat. Add the garlic and cook until golden brown, about 3 minutes. Add ½ cup dry white wine and boil until the wine is almost evaporated, about 3 minutes. Add 1 pound raw tiny shrimp and cook until the shrimp are pink, about 4 minutes.

Remove the skillet from the heat. Add ¼ cup parsley, lemon juice, and ¼ teaspoon of the kosher salt. Stir to combine and season as needed.

In a medium bowl, combine 3 cups ricotta cheese, ¾ cup finely grated Parmesan cheese, the remaining 1 teaspoon kosher salt, and ¼ teaspoon black pepper. Stir to combine and season as needed.

Spread ½ cup of the cream sauce in the bottom of a 9x13-inch baking dish. Arrange ⅓ of the noodles over the cream sauce. Spread half the ricotta mixture over the noodles. Evenly arrange half the shrimp mixture, lobster, and crab. Sprinkle with 1 cup mozzarella.

Dollop and spread 1 cup of the cream sauce over the cheese. Repeat layering with half the remaining noodles, remaining ricotta mixture, remaining shrimp mixture, lobster, and crab. Sprinkle with 1 cup mozzarella cheese and dollop with 1 cup cream sauce. Top with remaining noodles, spread with remaining cream sauce, and sprinkle with remaining 2 cups mozzarella.

Coat a large sheet of aluminum foil with cooking spray. Loosely cover the baking dish with the foil, spray-side down. Bake for 30 minutes. Uncover and bake until golden-brown and bubbly, 20 to 25 minutes more. Let cool for at least 15 minutes before slicing. Garnish with the reserved parsley before serving.