In a small saucepan, combine 2 cups water with the sugar and thyme; bring to a boil over high heat, stirring occasionally, until sugar has dissolved. Remove from heat; let cool to room temperature.
Pour mixture through a fine sieve into a large glass measuring cup; discard thyme. You should have 2 cups syrup. Cover with plastic; chill.
In a large serving pitcher, stir together lemon juice, vodka, and chilled syrup; garnish with thyme. Divide evenly among eight tumblers filled with ice; serve immediately.