Preheat the oven to 350°F. Grease a 9×5-inch loaf pan and line it with parchment paper, leaving a bit of overhang on two sides.
In a large bowl, beat the self-rising flour, granulated sugar, unsalted butter, eggs, and lemon zest with an electric mixer on medium speed until the batter is light and fluffy, about 2–3 minutes.
Spread the batter evenly in the prepared pan and smooth the top with a spatula.
Bake for 45–50 minutes, until the top is golden brown, the cake feels springy, and a toothpick inserted into the center comes out clean.
Meanwhile, in a small bowl, stir together the remaining granulated sugar and fresh lemon juice until the sugar is mostly dissolved.
When the cake comes out of the oven, poke holes all over the top with a skewer or fork, then pour the lemon drizzle over the hot cake, letting it soak in.
Let the cake cool completely in the pan on a wire rack. Use the parchment overhang to lift it out, slice, and serve.