Bring 6 cups water, sugar, thyme, cinnamon sticks, lime juice and lime zest to a boil in a 5-quart saucepan over medium-high heat. Remove the pan from the heat and add the tea bags. Steep the tea for 15 minutes. Remove the tea bags and allow the mixture to cool to room temperature, about 1 hour. Strain the mixture into a pitcher and refrigerate until ready to serve.