Preheat the oven to 350ºF. Butter and line an 8x4 inch loaf pan with parchment paper (leave some paper hanging on two sides, it will help to remove the lemon drizzle cake from the loaf pan).
In a mixing bowl, mix together eggs, self-rising flour, granulated sugar, softened unsalted butter, and freshly grated lemon zest using an electric mixer. Beat until combined and creamy. Then, transfer the lemon cake batter to the prepared loaf pan. Spread evenly. Bake in the preheated oven for 40-45 minutes or until golden and ready. Check the readiness of the lemon drizzle cake using a toothpick inserted in the center, if it comes out clean - the cake is ready.
While the lemon drizzle cake is baking, you can prepare the lemon drizzle. In a bowl, whisk together freshly squeezed lemon juice and powdered sugar until thicken and smooth.
Remove the loaf pan from the oven. Poke holes all over the cake using a skewer. Then, evenly pour the lemon drizzle over the lemon cake. Let the cake cool slightly. Then, remove the lemon drizzle cake from the loaf pan using hanging parchment paper, slice, and enjoy!