Crack 2 eggs into a mixing bowl. Add 1/2 cup of sugar to the eggs. Beat the eggs and sugar until the sugar completely dissolves.
Pour 1/4 cup of oil into the egg and sugar mixture. Beat the mixture for an additional 3 minutes until well combined.
Incorporate 2 tbsp of lemon juice into the mix. Beat the mixture for 30 seconds.
Add 1/2 tbsp of lemon zest to the mix. Ensure you include only the green skin, avoiding the bitter white part beneath.
Using a strainer, add 1/2 cup of flour, 1/2 tsp baking powder, 1/4 tsp baking soda, and a pinch of salt to the mixture.
Use a beater to mix all the ingredients thoroughly. Beat for 1 or 2 minutes until a smooth batter is formed.
Grease a loaf pan with oil. Place a parchment paper in the loaf pan to prevent sticking. Pour the batter into the prepared pan.
Use a nonstick dish for baking. Place a Stainless Steel Trivet inside the dish. Preheat the dish for 5 minutes.
Position the loaf pan inside the preheated dish. Bake on low to medium heat for 40 minutes, ensuring even cooking.
In a separate bowl, mix 1/3 cup powdered sugar with 1 tbsp of lemon juice.
Pour the powdered sugar and lemon juice mixture over the baked cake, creating a delightful glaze. Sprinkle additional lemon zest over the cake for a burst of flavor.