In a small bowl, cream the coconut butter until smooth, about 3 to 5 minutes, with a hand blender on high speed.
Add half the confectioner's sugar, half the milk, and all the vanilla and lemon juice. Combine on medium speed with the hand blender until smooth and creamy.
Scrape down the sides of the bowl. Blend in the remaining confectioner's sugar in 1/4 cup increments, until you get the desired results. Blend in more milk to thin out, as necessary.