Prepare the lobster by using kitchen shears to carefully cut down the back of the shell. Remove the intestinal vein running down the tail and discard the gritty stomach sack. Extract the meat, chop into bite-sized pieces, and reserve the shells.
In a saucepan, simmer the reserved lobster shells in the heavy cream for 15-20 minutes to infuse the sauce with deep seafood flavor. Strain through a fine-mesh sieve and discard the shells.
Cook the bucatini in a large pot of salted boiling water until al dente. Reserve 1 cup of pasta water before draining.
In a large Dutch oven or skillet, melt the butter with the olive oil over medium heat. Sauté the minced shallots and garlic until translucent and fragrant.
Add the red pepper flakes and deglaze the pan with the white wine, simmering until the liquid is reduced by half.
Stir in the San Marzano tomatoes and the shell-infused cream. Simmer the sauce for 10 minutes until it thickens and emulsifies.
Gently add the chopped lobster meat to the simmering sauce and poach for 3-5 minutes until just opaque and tender, being careful not to overcook.
Toss the cooked bucatini into the sauce. Add the reserved pasta water a tablespoon at a time as needed to help the sauce perfectly coat the pasta.
Finish the dish by folding in the lemon zest, fresh basil, and parsley. Serve immediately, optionally topped with torn burrata cheese.