Bring 1 bunch thyme and 1 1/2 cups each sugar and water to a simmer in a saucepan over medium heat, stirring until the sugar dissolves. Let cool, then strain the syrup into an ice-filled pitcher. Stir in 2 cups each fresh lemon juice and cold water. Serve over ice with thyme sprigs and lemon slices.
Photograph by Kana Okada