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For the pasta: Bring a large pot of salted water to a boil. Cook pasta until al dente. Reserve ½ cup of pasta water before draining.
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Sauce: In a large skillet, heat the butter and olive oil over medium heat. Add shallot and garlic; sauté until fragrant and translucent (about 2 minutes). Pour in white wine; simmer until reduced by half.
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Add cream and cheese and lower the heat and stir in the heavy cream. Add Parmesan cheese and whisk until melted and smooth. Season with salt, pepper, and optional red pepper flakes. Add lobster and gently fold in the lobster meat; cook 2–3 minutes, just to warm through (don’t overcook or it’ll toughen).
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Add drained pasta to the pan. Toss well, adding reserved pasta water a bit at a time until the sauce lightly coats the noodles. Finish with lemon zest, lemon juice, and parsley.
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Serve immediately
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Garnish with extra Parmesan, cracked pepper, and a drizzle of olive oil or butter if you like.