For the Cake: Adjust oven rack to middle position and preheat oven to 350°F (175°C). Using nonstick spray, generously grease a 9- by 5-inch loaf pan. Line pan with parchment cross-wise, allowing a 1-inch overhang on the longer sides of the pan.

In a medium bowl, sift together flour and salt. Set aside.

In the bowl of a stand mixer fitted with paddle attachment, beat butter and sugar on medium-high speed until pale and fluffy, about 2 minutes. Add the eggs, lemon juice, lemon zest, and vanilla paste and mix until fully combined, about 45 seconds. (Mixture will look slightly separated.) Add the dry ingredients and mix, pausing to scrape down the sides of the bowl with a flexible rubber spatula as needed, until just combined and no dry spots remain, about 30 seconds. Do not overmix. Using a flexible rubber spatula, spread batter into prepared pan. (Alternatively, the batter can be prepared in a large mixing bowl using an electric hand mixer.)

Bake until top of loaf is golden brown and a cake tester or skewer inserted in the middle comes out clean, 55 to 60 minutes. (Check the cake at the 40 minute mark; if the cake is becoming too dark, tent it with foil and continue to bake.) Remove cake from oven. Using a cake tester or skewer, prick the top of the cake about 15 to 20 times; set aside.

For the Drizzle: In a spouted measuring cup, whisk sugar and lemon juice until a cloudy syrup forms. (The sugar should not be dissolved.) Drizzle over still-hot cake, distributing mixture evenly across entire surface to adequately soak the loaf. Using a flexible rubber spatula, scrape any remaining granulated sugar from the cup and onto the cake, taking care to spread it evenly across the loaf.

Set pan on a wire rack and allow cake to cool completely, until bottom of pan is cool to the touch and a white crystallized topping has formed on top of the cake, about 3 hours. Lift parchment to remove cake from pan. Slice with serrated knife and serve at room temperature.