Dampen the rim of the martini glass and then dip it in sugar to coat it. Chill the martini glass in the freezer.
Use a peeler to peel a swath of lemon going around the lemon to get it as long as possible. Use a cocktail pick to poke two holes in the swath then put the lavender stem through it. Refrigerate until ready to use.
In the bottom of a cocktail shaker, add the vodka, lemon juice, lavender simple syrup, and the pinch of salt. Fill the rest of the shaker with ice and shake vigorously for twenty seconds then strain into the chilled martini glass. Serve immediately with the lemon swath garnish.