Preheat the oven to 170°C. Grease and line a loaf pan with parchment paper.
Sift together the flour, baking powder and salt into a bowl.
In another bowl whisk together the yoghurt, sugar, eggs, vanilla, lemon zest & juice. Add the oil and combine.
Slowly add the flour mixture to the wet ingredients, combining gently.
Pour the batter into the loaf pan and bake for about 45-55 minutes, until golden and a skewer inserted in the middle of the loaf comes out clean.
When the cake is done, take it out of the oven and rest for 10 minutes in the tin then turn it out onto a wire rack.
If you want icing, mix some lemon juice and icing sugar until you get a thick, pourable glaze. Pour this over the warm cake the and let it cool completely.