Combine the sugar, thyme, and 1 cup water in a small pot. Bring to a boil and cook, stirring occasionally, until the sugar is dissolved. Let cool and discard the thyme.
Combine the thyme syrup with the strawberries, lemon juice, and 5 cups cold water in a large pitcher. Chill for 30 minutes or up to 12 hours. Serve over ice, garnished with additional thyme. Add a splash of vodka, if desired.
This was a big hit with everyone. Delicious and different. We didn't add vodka, but I am serving it at my next adult party with a splash of vodka.