Cook pasta shells in a large pot of water with the tablespoon salt until just tender. Reserve 1/2 cup pasta water, then drain.
While the pasta cooks, melt butter in a large saucepan over medium heat. Cook shallot for 3 minutes, stir in flour for 1 minute, then gradually whisk in milk.
Add sauce salt and white pepper and simmer gently for 3 minutes. Add raw lobster pieces and cook at a gentle simmer for 4 to 6 minutes, stirring carefully, until opaque and 145°F in the largest pieces.
Remove from the heat and fold in Gruyere and fontina until melted. Stir in lemon juice.
Fold in the pasta shells, adding reserved pasta water a little at a time only if the sauce needs loosening. Serve immediately.