For the shrimp, crab and lobster linguine: Bring a pot of water to a boil. Add the grapeseed oil and 2 tablespoons salt. Add the linguine and cook according to package instructions. Drain and set aside.
Coat a large skillet over medium-high heat with the butter. Sprinkle the shrimp with salt and pepper. Add the garlic and shrimp to the skillet and cook until the shrimp is pink, 1 minute. Add the fine crabmeat and lump crabmeat; mix well for 1 minute. Add the lobster and cook, stirring, until all the seafood is heated through, another minute. Remove the pan from the heat and set aside.
For the white sauce: Melt the butter in a large saucepan. Add the onion and garlic; cook until tender, 3 minutes. Add the flour, 1 teaspoon salt and 1/4 teaspoon pepper; mix well. Slowly stir in the half-and-half. Add the Parmesan and cook until the sauce thickens, 4 minutes.
To serve: Divide the pasta among 4 serving bowls. Add the seafood medley. Top with white sauce, sprinkle with Parmesan and garnish with basil.