Bring a large pot of water to a boil over high heat. Season it generously with salt. Add the sliced lemons and blanch for 30 seconds. Using tongs, remove the lemons to a paper towel-lined plate to drain. Dry well.
Heat a large skillet over medium-high heat. Add the olive oil and heat another 30 seconds. Add the shallots and garlic to the skillet and season with 1/2 teaspoon salt. Cook, stirring often with a wooden spoon, until fragrant and beginning to brown slightly, about 2 minutes. Add the capers, anchovy paste, red pepper flakes and the blanched lemon slices and cook, stirring occasionally with a wooden spoon to dissolve the anchovy paste and brown the lemons, for another 2 minutes. Add the zucchini and remaining teaspoon salt. Cook, stirring occasionally, until parts of the zucchini turn deep brown while some parts remain al dente, about 10 minutes.
Meanwhile, add the pasta to the boiling water and cook for 2 minutes less than package directions, about 8 minutes. Add 1/3 cup pasta water to the skillet with the zucchini and stir to deglaze. Use a pair of tongs to remove the pasta directly to the skillet. Sprinkle the bare pasta with the Parmesan and toss well to coat the pasta with the zucchini sauce. (Some of the zucchini should have gotten rather soft, which helps to create a silky sauce.) Add another 1/2 cup pasta water if needed to maintain the sauce. Top the pasta with the herbs and feta and serve.