Tender lobster, spaghetti, and plenty of sliced garlic come together in a buttery, lemony sauce for a special-feeling pasta dinner that’s ready in about 40 minutes. Fresh herbs brighten every bite, while a splash of reserved pasta water helps the sauce cling beautifully to the noodles.
Bring a large pot of water to a boil. Generously salt the water once it is boiling.
If using raw lobster tails, use sharp kitchen scissors to cut through the top and bottom of each shell toward the fin, taking care not to cut the meat or fin. Open the shells and gently remove the meat. Rinse away any debris, pat dry, and cut the meat into 1-inch pieces. Season with 1 teaspoon kosher salt and a few twists of black pepper. If using cooked lobster meat, cut it into bite-sized pieces and season.
Add the spaghetti to the boiling salted water and cook until al dente, stirring occasionally. Before draining, reserve about 1 cup of the starchy pasta water. Drain the pasta without rinsing.
While the pasta cooks, melt the butter with the olive oil in a large skillet over medium heat. Add the shallot, sliced garlic, and lemon peel. Season with ½ teaspoon kosher salt and a few twists of black pepper. Cook, stirring occasionally, until softened and fragrant, about 5–6 minutes.
Stir the stock and vinegar together, then add the mixture to the skillet. Simmer for 1–2 minutes. Add the lobster and stir to coat it in the aromatics. Reduce the heat to medium-low and cook, stirring occasionally, until raw lobster is just opaque and tender, about 3–4 minutes. If using cooked lobster, heat it gently just until warmed through. Remove the skillet from the heat if the pasta is not ready, so the lobster does not overcook.
Return the skillet to medium-low heat if needed. Add the drained pasta and toss well. Simmer for 1–2 minutes, until the pasta absorbs some of the sauce. Add reserved pasta water a splash at a time if the sauce needs loosening; simmer briefly if it needs to thicken. Remove the lemon peel, then toss in the lemon juice and fresh herbs.
Divide the pasta among bowls. Finish with extra lemon juice and chopped herbs, and serve immediately.