Heat milk to steaming, being careful not to scorch. Add lavender and steep until milk comes back down to room temperature, then strain to remove lavender flowers.
Beat butter, powdered sugar, lavender milk, vanilla and salt in a large mixing bowl until smooth. Add lemon zest and juice if using and beat again. Keep covered until ready to use - icing will dry and form crust quickly.
Notes
Cooling the lavender steeped milk can be expedited by putting it in the refrigerator after the lavender has steeped for at least 5 minutes. Remove once milk is at room temperature. If you leave it to get too cold, it will make your icing harder to beat together.