Pre-heat oven to 180°C (160°C fan-forced). Line oven trays with baking paper.
Place butter and icing sugar in the large bowl of an electric mixer. Beat until pale and creamy.
With the mixer on low speed, gradually add the flour, vanilla and lemon rind. Mix until well combined. Remove from the mixer and bring dough together with your hands.
Roll tablespoon measures of dough into balls and flatten slightly when placed on trays. Press lightly with a fork and bake for 18 minutes. Allow to cool on tray for 5 minutes before removing to a cooling rack to cool completely.
For the icing, cream the butter and icing sugar together, then add in the lemon juice, mixing until smooth.
Once cooled, spoon a little icing between biscuits and sandwich together.