If using raw lobster tails, steam them for 4–5 minutes until the shells turn bright red and the meat is opaque. Cool slightly, remove the meat from the shells, and cut into bite-sized pieces. If using cooked lobster meat, simply chop it into pieces.
Place the lobster meat in a bowl and toss with the lemon zest and 2 tablespoons of chopped parsley.
Bring a large pot of salted water to a boil and cook the pasta until just shy of al dente. Reserve ½ cup of the pasta cooking water before draining.
Heat the olive oil in a large skillet over medium heat.
Add the diced shallots and 1 teaspoon of kosher salt. Cook for about 5 minutes until softened and translucent.
Pour in the seafood broth (or chicken broth with lemon juice) and simmer for 2–3 minutes until mostly reduced.
Stir in the garlic and cherry tomatoes.
Increase the heat to medium-high and cook for about 10 minutes, stirring occasionally, until most of the tomatoes burst and create a fresh sauce.
Reduce the heat to medium-low and gently stir in the lobster meat.
Add the cooked pasta and ¼ cup reserved pasta water. Toss everything together until the pasta is lightly coated. Add additional pasta water if needed.
Remove the skillet from the heat and stir in the fresh lemon juice.
Serve the Lobster Pasta with Lemon and Cherry Tomatoes topped with the remaining parsley, a drizzle of olive oil, flaky sea salt, red pepper flakes, and freshly grated Parmesan if desired.