First, in a small bowl, combine sugar and the zest of two lemons. Using your fingertips, rub the ingredients together. This will help bring out the oils in the zest, adding more flavor.
In a large bowl, whisk together the flour, baking powder, and salt.
In a separate mixing bowl, add unsalted butter. Using a handheld mixer, whip the butter on high speed until smooth and creamy (about a minute). Make sure it is at room temperature. The butter needs to be soft.
Next, add lemon sugar and beat on high speed for 2 minutes until the butter and sugar are combined. Use a rubber spatula to scrape the sides and bottom of the mixing bowl as needed while mixing.
Continue by adding one egg at a time while still beating.
Add the sour cream, milk, lemon juice, and vanilla extract, then beat on medium speed until combined. It’s essential not to overmix the batter to avoid a heavy, dense lemon pound cake. The mixture may look curdled as a result of the varying textures combining; don’t panic, this is normal.
Preheat the oven to 350°F. Lightly spray a 9x5-inch loaf pan with baking spray and line it with parchment paper.