Preheat the oven to 325°F.
In the bowl of your stand mixer add your unsalted butter. Using your paddle attachment, beat the butter on medium speed for about 30 seconds to loosen up the butter.
Add the sugar and salt, and beat on medium speed with the butter, salt, and sugar until well combined.
Pause and scrape down the sides of the bowl so the butter and sugar are well combined.
Add the lemon zest, vanilla extract, and lavender. Mix until combined.
Slowly add the flour by adding ½ cup at a time to start allowing the flour to incorporate with each add.
Turn the dough out onto the piece of parchment paper and form the dough into a log.
Roll the parchment up to create a log. Place in the fridge and chill for 30 minutes.
Line a baking sheet with a piece of parchment paper or a reusable silicone mat.
Remove the dough from the fridge and remove the piece of parchment paper. Cut the dough into ½” disks using a bench scraper, pastry cutter, or a butter knife and place them on the prepared baking sheet 1 inch apart.
Bake at 325°F for 20 minutes or until the sides have turned golden brown.
Meanwhile, add the powdered sugar to a bowl and slowly add the lemon juice, 1 tablespoon at a time, stirring between each addition until you get the desired consistency.
Once the cookies are done baking, remove them from the oven and transfer the cookies to a cooling rack.
Allow cookies to cool for about 15 minutes.
Dip one side of the cookies into the icing and place them on the cooling rack so the icing can settle.
Optionally you can sprinkle with additional lavender.
Store your cookies in an airtight container at room temperature. Your cookies will stay fresh for 3-4 days.