Bring a large pot of salted water to a boil and cook pasta according to package instructions until al dente. Drain and reserve at least ½ cup of pasta water.
In a large skillet over medium heat, add about 2 tablespoons of olive oil and the minced shallot. Sweat until translucent, then add the minced garlic. Once garlic is softened and fragrant, add the cherry tomatoes and cook until they begin to blister. Then, add the white wine (off of the flame, but while pan is still hot) and use a wooden spoon to scrape any bits off of the pan.
Add in the uncooked lobster meat, the minced tarragon, and the heavy cream. Sauté lobster meat until cooked through.
Lower the heat, then add the butter and stir until emulsified, then stir in the lemon zest. Simmer on low.
Add the cooked pasta to the sauce and toss to combine. Season with salt and pepper and, if necessary, add any more pasta water or cream until the sauce is the consistency you like.
Garnish with more lemon zest or lemon juice, fresh chopped chives, and red pepper flakes. Parmesan cheese is optional on top.