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In the bowl of an electric mixer fitted with the paddle attachment, beat on medium speed (I use #4 on my KitchenAid mixer) the butter until it is smooth and very creamy, about 1-2 minutes.
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Add the confectioners' sugar and beat for another 2 minutes. Beat in the vanilla extract, then stir in the dried lavender and lemon zest.
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Stir in the dry ingredients and mix until they are incorporated. Make a ball of the dough and seal in plastic wrap. Once in the wrap, flatten the dough into a disk and chill for one hour (at least--can be longer).
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When you're ready to roll and cut the cookie dough, preheat oven to 350°F and place the oven rack in the middle position. Line 2 baking sheets with parchment paper or two baking mats.
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Roll the dough 1/4" thick on a lightly floured surface or between two sheets of parchment paper. Cut desired shapes, place on baking sheets and chill in the refrigerator or freezer for about 15 minutes.
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Bake until very light golden brown, about 8-10 minutes. Let cool on cookie sheets on wire racks.