Boil water in large stock pot and prepare pasta to package directions, until al dente - leaving it slightly chewy.
In a large skillet, while lobster cooks, melt butter.
Add shallot and garlic, cook until soft and fragrant, about 1 minute, stirring frequently.
Add in lobster and toss in butter.
Stir in salt, lemon juice, lemon zest, and wine.
Remove 1/2 cup pasta water before draining, and mix into sauce.
Bring to a boil, and reduce heat to simmer.
Let sauce thicken while draining pasta.
When sauce has thickened slightly, stir in pasta and tarragon, and toss.
Heat additional 1-2 minutes.
Serve and enjoy!