Thaw shrimp fully under cold running water if frozen, then peel and devein. Pat completely dry with paper towels and season with 1/4 tsp salt and 1/8 tsp black pepper.
Use a Microplane to zest 1 tsp of lemon zest from the lemons first, then cut and juice them to yield 1/3 cup of fresh lemon juice. Set both aside in a small bowl.
Bring a large pot of water to a rolling boil, salt generously, and cook linguine according to package directions until al dente. Before draining, reserve 1/2 cup of starchy pasta water, then drain and set aside — do not rinse.
Heat the skillet over medium-high heat, add 1 tbsp butter and 1 tbsp olive oil, then cook the shrimp in a single layer for 1-2 minutes per side until pink and just opaque. Transfer to a plate and set aside.
Reduce heat to medium, add the remaining 1 tbsp olive oil to the same skillet, then add the minced garlic and red pepper flakes. Stir constantly for 30-45 seconds until fragrant and just golden.
Pour in the white wine and scrape up any browned bits from the pan. Let simmer for 2-3 minutes, stirring occasionally, until reduced by about half.
Add the lemon juice and lemon zest, stir to combine, then add the remaining 3 tbsp of butter one tablespoon at a time, stirring continuously after each addition until the sauce is glossy and emulsified. Season with remaining salt and pepper.
Add the drained pasta to the skillet and toss with tongs until every strand is coated. Add reserved pasta water a few tablespoons at a time if the sauce is too thick.
Return the seared shrimp to the pan along with any collected juices, fold gently into the pasta, then sprinkle in the freshly grated Parmesan and toss to incorporate.
Divide among warm bowls, top with fresh chopped parsley and lemon slices, and serve immediately with extra Parmesan on the side.