Boil the cavatappi in water with 1 teaspoon salt for 3 minutes less than the package directs and drain.
Melt the butter, whisk in the flour for 1 minute, and gradually whisk in the warm milk and evaporated milk until the sauce thickens.
Combine the pasta, sauce, pepper and remaining salt in a buttered 6-quart crockpot and cook on low for 45 minutes.
Stir in the white cheddar and Gruyère by handfuls and cook on low for 30 minutes more.
Fold in the lobster and lemon juice and cook on high for 15 minutes until the lobster reaches 165°F.