Step 1 With a food processor running, drop the lavender through the tube. Add sugar and lemon zest, and pulse until combined, then add flour and salt and pulse.
Step 2 Add butter and pulse until just incorporated. Continue pulsing while adding the lemon juice through the tube, just until dough forms a ball.
Step 3 Roll the ball into a log about 10 inches long, wrap in plastic and chill for at least 1 hour. (Dough can be frozen for up to 1 month — slightly thaw before cutting and baking.)
Step 4Heat the oven to 350 degrees. Slice the log crosswise into one-half-inch slices and arrange on an ungreased baking sheet, spacing the cookies about 2 inches apart. Bake until the edges are golden brown, 20 to 25 minutes. Cool the cookies on a rack.