This is a tough one because the pasta and the lobster are two different ingredients, so the sauce can either compliment or be a bust.
I would lean to the lobster side of things because it is the stronger taste.
I think a seafood sauce right off the shelf would do the trick. Or you could have two sauces on the same plate.
Why not put the sauces out and let the guests pick the one they like?
I like the Alfredo idea.
I have an old cookbook. Here's a recipe for a Tartare Sauce if you want to be a bit more daring.
Combine 1 cup Mayonnaise, 1 teaspoon grated onion, 1 tablespoon minced dill pickle, 1 teaspoon minced parsley and 1 teaspoon chopped pimento.
I think a choice of sauces would be more fun.
Serve with Red Wine and send me an invitation.