If using a whole cooked lobster, remove the meat from the shell. Chop the lobster meat into bite-sized pieces and set aside. If using crayfish, follow the same procedure.
In a large pot, bring salted water to a boil. Add the spaghetti and cook according to package instructions until al dente. Reserve 1 cup of pasta water, then drain the spaghetti and set aside.
In a large skillet, heat the olive oil over medium heat. Add the chopped onion and celery, sauté for about 5 minutes until soft and translucent. Add garlic and crushed red pepper flakes, cook for an additional 1-2 minutes until fragrant.
Add the tarragon and low sodium broth to the skillet, bring to a simmer. Cook for 5-7 minutes to reduce slightly. Stir in the heavy cream and lemon zest, simmer gently for another 5 minutes until the sauce thickens.
Add the cooked spaghetti and lobster meat to the skillet, tossing to coat in the creamy sauce. If sauce is too thick, gradually add reserved pasta water to reach desired consistency. Stir in grated parmesan and season with salt and black pepper to taste.
Plate the Creamy Lobster Pasta, garnish with chopped chives and additional parmesan. Serve immediately and enjoy.