Heat the olive oil in a large skillet over medium heat. Add the chile flakes, garlic, Fresno chile and onions and cook until the onions are tender and fragrant, 5 to 7 minutes. Add the white wine and bring to a low simmer. Stir in the tomatoes, salt and pepper. Reduce the heat to low, cover and simmer until reduced slightly, 35 to 40 minutes.
Bring a large pot of water to a boil. Add the spaghetti and cook until al dente according to the package instructions. Reserve 1/2 cup pasta water, then drain the pasta and keep warm.
Add the lobster tails to the sauce, cover and cook for about 5 minutes (they will not be cooked through at this point). Remove the lobster to a cutting board and carefully use a knife to split open the tails on the backside. Remove the meat and coarsely chop.
Add the lobster meat back to the sauce along with a few tablespoons of the pasta water and the spaghetti. Toss to coat, adding more pasta water if the sauce is too dry. Toss in the parsley and mint. Drizzle with a good-quality extra-virgin olive oil, if desired. Serve immediately.