Line the muffin tin with the paper cases. Put all the cake ingredients into a bowl, and beat with an electric whisk until evenly combined and smooth.
Make the icing: put the butter and half of the icing sugar into a bowl, and beat with an electric whisk until evenly combined and smooth. Add the lemon juice and the remaining icing sugar, and beat again until light and fluffy.
Spread the icing over the cold cup cakes, and decorate with a slice of lemon.