Beat the butter and cream cheese on medium-high speed for 5 minutes, stopping to scrape the bowl once or twice.
Reduce the speed to low and gradually add the powdered sugar. Once all of the powdered sugar is incorporated, add lemon juice, one tablespoon at a time, till icing is soft and fluffy. Add vanilla and beat at a low speed until incorporated, then increase to medium-high and beat for another five minutes. If icing is too thin, add a bit more powdered sugar, if too thick, add a bit more lemon juice or milk.
This recipe is enough to frost a 2 or 3 layer cake if icing is spread with a knife. If you like a thick icing or will be decorating your cake with the swirly piped icing (pictured), make a double batch as this method uses more icing.