Line a cookie sheet with parchment and preheat oven to 350F.
Blitz the lavender in a coffee/spice grinder until the buds are broken down a little but not so much they're powdered.
In the bowl of a stand mixer, mix melted coconut oil and powdered sugar until fully mixed. Add in non-dairy milk a tablespoon at a time, making sure to incorporate fully after each addition + remembering to scrape down sides. Then add extract and stir again to combine.
Add in the all purpose flour, lavender, salt, and soda and stir to partially combine. Add in rice flour and stir just until there is no dry flour remaining and a soft dough forms.
Dust your work surface and rolling pin with flour and roll out the dough immediately, to about 1/4" thickness. Cut into twelve cookies (or maybe more, my cookie cutter was a 3" circle).
Bake for 9-11 minutes. These cookies shouldn't brown much. Let sit for a few minutes on the cookie sheet to firm up before transferring to a cooling rack.
While they're cooling, prepare the glaze by adding lemon juice to sifted icing sugar and whisking until fully incorporated.
Once the cookies are fully cooled, dip the top of a cookie into the glaze, and let the excess run off for a moment before setting down + sprinkling with lemon zest and a few lavender buds.