Bring a large pot of water to a boil for the pasta. Add about a tablespoon of salt and keep at a simmer while you prepare the other ingredients.
In a large skillet that has a lid, melt the butter over medium high heat. Add the shallot and teaspoon salt and cook, stirring occasionally, about 2 minutes until softened. Add the tomatoes and cook over high heat for 2-3 minutes. Watch carefully as you don’t want the shallots to burn, but want a fairly high heat here so the tomatoes start to burst. When they look like they are just starting to break down and the pan is super hot, pour in the wine. Cook for a minute or two to let some of the wine cook off, then cover with the lid and turn to low.
While the tomatoes are simmering, add the pasta to your pot of boiling water and cook.
When the pasta is just one minute shy of being done, add the lobster meat to the tomatoes along with the lemon zest and capers (if using). Stir for a minute.
Use tongs to lift the pasta out of the water and put it directly in the pan with the tomatoes and lobster. Turn the heat back up to medium high. Stir, adding about ½ cup pasta cooking water. Cook over medium heat until the sauce is nicely thickened, about 1-2 minutes. Pour in the cream and stir to combine, making sure it is warmed through. Taste for seasoning and add salt if needed, and some freshly cracked black pepper.
Place the pasta on plates and garnish with the mint.