In your food processor, measure the flour, powdered sugar, salt, lemon zest and lavender. Pulse several times until well combined.
With the processor running, drop the butter down the chute, a tablespoon at a time, and process the mixture until moist and crumbly.
Add the vanilla extract and lemon juice, and process just until the dough comes together into a dough ball.
Dump the dough out onto a clean counter and gather any dry floury bits together, shaping the dough into a disk, and lightly dusting it with a little extra flour.
Line an 8 or 9 inch square baking pan with parchment paper. So that the paper doesn't slide around when you press in the dough, it helps to lightly grease the inside of the pan with butter, to get the paper to stick to the pan. Press the dough into an even layer into the pan.
Now cut the dough into squares, using a sharp knife or bench scraper, dipping it in flour in between cuts. I used a bench scraper, which I find easiest for cutting dough inside the pan. Cutting the dough before baking makes it much easier to cut without breaking it after it comes out of the oven. For an 8-inch pan, cut the dough into 5x5 sections, for 25 cookies. For a 9-inch pan, you can cut the dough a bit smaller, into 6x6 sections, for 36 cookies.
Use a toothpick, skewer or cake tester to prick the dough all over - this is called "docking the dough", and helps prevent it from puffing up as it bakes.
Refrigerate the shortbread for 30 minutes.