In a small bowl, whisk together the milk, vanilla, lemon juice, and zest.
In a standing mixer fitted with the paddle attachment, or with a hand-held electric mixer and a bowl, combine the butter and sugar and mix on low until incorporated. Raise the speed to high and mix until light and fluffy, about 10 minutes. (Occasionally turn the mixer off, and scrape the sides of the bowl down with a rubber spatula.)
Reduce the speed of the mixer to low. Add the milk mixture in 3 batches, waiting for each batch to be fully incorporated before adding the next (scrape the bowl down occasionally). Raise the speed to high and mix briefly until fluffy. Use as desired. May be stored, covered, in the refrigerator for 3 days.
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