Bring a large pot of heavily salted water to a boil over high heat. Meanwhile, finely grate the zest of the lemons on a Microplane; set the zest aside. Quarter 1 of the lemons (reserve the second zested lemon for another use). Add the pasta to the pot and cook until al dente.
Meanwhile, melt the butter in a large nonstick frying pan over medium-high heat. Add the lemon pieces, cut-side down, and sear until both cut sides are browned, about 2 minutes per side. Remove the lemon pieces from the pan and juice them when cool enough to handle. Discard the juiced lemon pieces.
Add the cream to the pan and bring to a simmer. Add half of the Parmesan, salt, and pepper; stir to combine; and remove the pan from the heat.
Reserve 1 cup of the pasta water and drain the pasta. Add the pasta, the remaining Parmesan, reserved lemon juice, and 2/3 cup of the pasta water to the pan of sauce. Place the pan over low heat and toss until the cheese is melted, adding more pasta water as needed to reach the desired sauce consistency.
Remove the pan from the heat and toss in the reserved lemon zest and dill. Taste and season with more salt and pepper as needed.