Bring a large pot of salted water to boil. In the meantime, zest, then juice, both lemons into a small container. Add pasta to water once it is at a rolling boil. Drain pasta when desired consistency is reached, reserving one cup of the pasta water on the side. Using the now empty pasta cooking pot, immediately add the butter, oil and set over a low flame. Once butter is melted, add pasta, lemon zest mixture and cheese and stir vigorously.
Once everything is incorporated, turn off flame and taste. Add salt and pepper as needed. Serve immediately, garnish with some extra parmigiano.