Bring a large pot of salted water to a boil. Add the spaghetti and cook until al dente. Reserve ½ cup of pasta water, then drain.
(Optional) Toast the breadcrumbs:In a small pan over medium heat, warm the olive oil. Add the panko and a pinch of kosher salt. Toast for 3–4 minutes, stirring often, until golden. Remove from heat and mix in the lemon zest and herbs. Set aside.
In a small pan over medium heat, warm the olive oil. Add the panko and a pinch of kosher salt. Toast for 3–4 minutes, stirring often, until golden. Remove from heat and mix in the lemon zest and herbs. Set aside.
In a large skillet over medium heat, melt the butter with the olive oil. Add the garlic and shallot and cook for 2–3 minutes, until soft and fragrant.
Add the cherry tomatoes and cook for 4–5 minutes, stirring occasionally, until blistered and some begin to burst. Use the back of your spoon to gently smash a few.
Pour in the white wine and simmer for 2–3 minutes. Stir in the lemon zest, lemon juice, lobster meat, and 1½ teaspoons kosher salt. Season with black pepper and cook for 1–2 minutes, just to warm the lobster through.
Add the cooked spaghetti and a splash of reserved pasta water. Toss with tongs until the sauce evenly coats the pasta. Add more pasta water if needed. Stir in the herbs and serve right away.