If you want a sugared rim, place coarse sugar on a small plate and moisten rim of coup glass (or other small cocktail glass) with a little grapefruit juice. Place glass upside-down on plate to coat rim in sugar.
Fill a cocktail shaker halfway with ice and add grapefruit juice, vodka, and Lillet Blanc.
Shake well and pour into prepared glass.
Garnish cocktail with small grapefruit wedge and a sprig of thyme or orange peel.