Add in the milk, lemon juice, zest, and vanilla extract.
Whisk well to combine.
Add in the flour, sugar, baking powder, and salt. Whisk well to combine.
Microwave the cake for 60 seconds. It should be cooked in this time. If the top is still very wet, you can microwave for an additional 15 seconds.
Make the frosting while the mug cake cools.
Mix together the butter, cream cheese, powdered sugar, and lemon juice.
Whisk well.
Add in the heavy cream as needed to get a smooth consistency. Top on the mug cake
Notes
The mug cake will continue to cook for a while before it finally cools, be careful of overcooking the cake as it will dry out. The top should be set and not wet, but it may appear still a little moist. Wait for the cake to cool before adding the frosting.