Add the granulated sugar and dried lavender buds to a food processor. Process for 10-15 seconds until the lavender is finely ground. Taste and adjust with more lavender if needed.
Add the lemon zest to the lavender sugar and process until the mixture resembles wet sand.
In a stand mixer fitted with the paddle attachment, or using an electric hand mixer, beat the softened butter and lemon lavender sugar together on medium speed until well combined, about 3-4 minutes.
Gradually mix the flour and salt into the wet ingredients until just combined. Cover the dough and chill in the refrigerator for 30 minutes.
While the dough chills, preheat the oven to 350°F (177°C). Line two large baking sheets with parchment paper.
Scoop about 1 tablespoon (15 ml) of cookie dough onto the prepared baking sheet, using a small cookie scoop for uniformity.
Bake the lavender cookies for 12-14 minutes, or until the bottoms are lightly golden brown.
Remove the cookies from the oven and allow them to cool on the baking sheet for 3 minutes before transferring them to a cooling rack to cool completely.
To make the lemon glaze, mix 2-3 tablespoons of lemon juice with 1-1½ cups of powdered sugar until well combined.
Top each cooled cookie with the lemon glaze, and sprinkle with finely chopped dried lavender if desired.