In a medium bowl, combine the sifted powdered sugar, whole milk, pure vanilla extract, and lemon juice.
Whisk the ingredients together until the mixture is smooth and free of lumps.
If the icing is too thick, add additional milk, one teaspoon at a time, until the desired consistency is reached for spreading or drizzling.
If the icing is too thin, add more powdered sugar, one tablespoon at a time, until it thickens appropriately.
Use immediately to ice shortbread cookies by spreading or drizzling the icing over cooled cookies.
Allow the icing to set at room temperature for about 30 minutes before serving or storing.