Preheat the oven to 180°C. Grease and flour 2 loaf pans.
Prepare the dry ingredients. Sift together the flour, baking powder, baking soda, and salt in a bowl, and keep to side.
Prepare the wet ingredients. In a small bowl, combine lemon juice, lemon zest, yoghurt, and vanilla.
In a stand mixer, cream the butter and sugar with the paddle attachment until light and fluffy, about 5 minutes. Add the eggs, 1 at a time and mix until the batter has a smooth and creamy consistency.
Alternatively, add the dry ingredients and the wet ingredients to the batter.
Evenly pour the batter into the two loaf pans. Bake for 50 to 60 minutes.
Prepare the lemon syrup. Combine sugar with lemon juice in a small saucepan and cook over low heat until the sugar dissolves. When the cakes are done, remove the cakes from the oven and spoon the lemon syrup over them. Allow the cakes to cool completely.
For the glaze, combine the icing sugar, lemon juice and lemon zest in a bowl. Remove the cakes from the pan and place them on a rack set over a tray or sheet pan. Drizzle the glaze over the cakes.