Stir in cooled mixture. Pour over ice or cover and refrigerate until ready to serve.
Add lemon juice and 4 cups of water to a medium pitcher.
In a small saucepan add sugar and 1 cup of water. Wrap 5 sprigs of fresh thyme in bakers twine and place in saucepan. Cook over medium heat, stirring occasionally until sugar is completely dissolved. Remove from heat and allow to cool. Once cooled, discard thyme.