Cool pasta in a large pot of boiling, generously salted water, stirring occasionally, until very al denote, about 2 minutes less then package directions (pasta will finish in the sauce).
Meanwhile, heat half of the butter in a large Dutch oven or other heavy pot over medium until melted. Add lemon slices and cook, stirring often, until softened and bottom of the pot is browned in spots 5-7 minutes. Using tongs, transfer one-third of lemon slices to a plate; set aside.
Just before pasta is al dente, scoop out 2 cups pasta cooking liquid. Add 1 1/2 cups pasta cooking liquid to butter sauce, (this may seem like a lot of liquid, but it will thicken once the remaining ingredients are added.) Add remaining butter a piece at a time, whisking until each piece is incorporated before adding more, until the sauce is emulsified and creamy.
Drain pasta and add to sauce. Cook, stirring often and adding 1 oz Parmesan a little at a time. Once all the cheese is added, continue to cook, still stirring, until cheese is melted and sauce is creamy and clings to pasta, about 3 minutes. Remove from heat and sprinkle with an almost ridiculous amount of pepper. Toss once more.
Serve with more lemon and Parmesan