In a medium bowl, combine the sifted powdered sugar, whole milk, pure vanilla extract, and lemon juice.
Stir the mixture with a whisk or spoon until smooth and glossy, ensuring there are no lumps.
If the icing is too thick, add more milk, a few drops at a time, until the desired consistency is reached for spreading or piping.
If the icing is too thin, add a little more powdered sugar to thicken it.
Use the icing immediately to decorate cooled shortbread cookies.
Allow the icing to set at room temperature for about 30 minutes before storing or serving.