Preheat your oven to 350°F (175°C). Lightly grease an 8-inch round cake pan, then line the bottom with a sheet of parchment paper to prevent sticking.
In a large bowl, cream together the sugar, softened butter, and egg yolks until light and fluffy. Stir in the Greek yogurt and finely grated lemon zest, mixing until the batter is smooth and well combined.
Gently fold the flour, baking powder, and salt into the wet mixture until just combined. Be careful not to overmix to keep the batter light.
In a separate bowl, whisk the egg whites until soft peaks form. Gradually and gently fold the whipped egg whites into the batter, being careful to maintain the airy texture.
Pour the batter into the prepared cake pan, spreading it evenly. Bake for 1 to 1¼ hours, or until the cake has risen, is golden brown, and a toothpick inserted into the center comes out clean. Allow the cake to cool in the pan for 10 minutes before transferring it to a wire rack. Peel off the parchment paper and let it cool completely.
Combine the sifted confectioners' sugar with the lemon juice in a small bowl, mixing until smooth. Pour the icing over the cooled cake, spreading it evenly with an offset spatula. Allow the icing to set before serving.