Zest one of the lemons onto a plate, then cut it in half and juice one half into a small bowl or cup. Reserve for later.
On the plate, pour the sugar over the lemon zest and rub them together with your fingers until the sugar is yellow and heavily aromatic.
Moisten the rim of a martini or coupe glass with a lemon half and press the rim of the glass into the sugar. Save the rest of the lemon sugar for future cocktails or desserts.
In a cocktail shaker full of ice, strain in the lemon juice, then add the vodka, Cointreau, and lavender syrup. Shake well for about 30-45 seconds, or until the shaker is too cold to hold anymore.
Strain into the rimmed glass.
Cut a long, thin strip of lemon rind off the remaining lemon. Take the piece of rind and gently form it into a coil with your fingers, then hold it there for about 20-30 seconds.
Add a stem of dried lavender flowers, cut to fit the glass. Release the coil and let the twist of lemon unfurl, then place it over the rim of the glass next to the lavender. Serve immediately.