In a medium bowl, mix the sugar with the chopped lavender and grated lemon zest. Using a handheld electric mixer, beat in the butter at moderate speed. At low speed, beat in the flour and salt until a soft dough forms. Transfer the dough to a sheet of wax paper and refrigerate for 20 minutes. Form the dough into a 4-inch log and chill for at least 45 minutes longer.
Preheat the oven to 350°. Slice the shortbread dough into 1/4-inch-thick rounds and place the rounds on ungreased baking sheets. Freeze the rounds for 10 minutes.
Bake the shortbread for 20 to 25 minutes, or until the edges are lightly browned. Transfer the baked shortbread to a wire rack to cool completely.
The cookie-dough log can be frozen for up to 1 month. Thaw slightly before slicing. The baked shortbread can be stored in an airtight container for up to 5 days.