Preheat oven to 325°F (160°C). Spray a 9×5-inches (23 x 12cm)loaf pan with nonstick cooking spray with flour.
In a medium bowl, sift together the flour, baking powder, and salt. Whisk the sour cream and lemon juice together in a small measuring cup.
In the bowl of a stand mixer fitted with the paddle attachment, combine the lemon zest and sugar. Rub together with your fingertips until the sugar is moist and fragrant. Add the butter to the bowl and beat the butter/sugar mixture on medium speed until very pale and fluffy, about 3-4 minutes. Scrape down the sides of the bowl.
Mix in the eggs in 3 additions, beating well after each addition until the mixture is smooth (stop to scrape down the sides of the bowl as necessary). With the mixer on low, alternately add the dry ingredients in 3 additions and the sour cream mixture in 2 additions, starting and ending with the dry ingredients.
Once all the ingredients have been added, scrape down the bowl then beat on low for another 30 seconds to fully combine. Use a rubber spatula to make sure the batter in the very bottom of the bowl is uniform.
Transfer the batter to the prepared pan. Smooth the top then tap the pan on your work surface to release air bubbles. Bake the cake for 55-65 minutes, or until a thin knife inserted near the center comes out with just a few moist crumbs. Transfer the pan to a wire rack and let the cake cool for 10 minutes, then turn it out.
While the cake is in the oven, make the syrup. Combine the sugar and lemon juice in a small saucepan and set over medium-high heat. Cook, stirring frequently, until the sugar dissolves. Bring the mixture to a simmer and allow to simmer for 2 minutes, then remove from the heat and set aside.
Once you've turned the cake out of the pan (the cake should still be warm), brush the top and sides with the lemon syrup. It'll seem like a lot, but use all of the syrup. Let the cake cool completely, about 2 hours.