Pre-heat the oven to 175°. Line or grease an 8x8" square tin.
Beat the butter and sugar together until fluffy.
Beat the eggs in, one at a time.
Combine the Greek yoghurt, lemon juice and milk and add to the butter/sugar, mixing just until incorporated.
Add the flour, baking powder and baking soda and mix just until everything is combined.
Pour out into the prepared pan and bake for around 25 minutes.
The cake is ready when an inserted skewer comes out clean. Remove from the oven and allow to cool for ten minutes or so, then turn out onto a wire rack to cool completely.
For the icing: mix the lemon juice with as much icing sugar as is needed. Drizzle all over the cooled cake. Slice into eight rectangles and enjoy!