In a shaker ½ full of ice, add gin, lemon juice, and honey-thyme syrup. Shake vigorously until very cold. Strain into highball full of ice and top with sparkling water. Drop in a lemon slice and sprig of thyme.
Bring ½ cup of water to boil. In a measuring cup or small bowl, add ½ cup of honey and boiling water. Stir. Drop in the thyme and allow to steep for 30 minutes.