In a small saucepan, combine the sugar and ½ cup water.
Bring to a boil, stirring occasionally, until the sugar is dissolved; let cool.
In a pitcher, combine the syrup with the lemon juice and 2½ cups water.
In a bowl, using a wooden spoon, mash the thyme with the lime juice.
Add to the lemonade and refrigerate for at least 1 hour.
Enjoy!