Heat the oil and butter in a large skillet over medium heat until the mixture begins to shimmer. Add the garlic and cook, stirring constantly, until soft and lightly golden brown, about 2 minutes.
Add the breadcrumbs, salt and pepper and cook, stirring occasionally, until golden brown and toasted, about 5 minutes; stir in the lemon zest. Transfer to a plate in an even layer. Set aside.
Bring a large pot of water to a boil. Add 2 tablespoons of salt and the pasta and cook, stirring occasionally, until just slightly under al dente, about 7 minutes. Reserve 1 cup of the pasta water and drain.
While the pasta is cooking, heat the oil in a large high-sided skillet over medium heat until it begins to shimmer. Add the garlic and cook, stirring, for 1 minute. Add the chile flakes and cook, stirring, 1 minute longer. Add the anchovy and stir constantly until it melts into the oil, about 1 minute longer.
Increase the heat to high, add the wine and cook until reduced by half, about 5 minutes. Stir in the lemon juice and bring to a simmer. Add the butter, piece by piece, whisking in each addition until smooth.
Add the pasta to the skillet and toss with tongs to coat. Add the lobster and some of the reserved pasta water, as needed, to thin the sauce. Add the basil, the 1/4 cup parsley, and the zest from 1 lemon and toss to combine. Season with salt and pepper.
Transfer the pasta to a large shallow serving bowl and sprinkle the breadcrumbs evenly over the top. Garnish with more lemon zest and chopped parsley, if desired, and serve.