Dust the lemon slices in the sugar, shaking off the excess. Grill until the sugar begins to caramelize and the lemon slices are lightly charred, 1 to 2 minutes per side. Let cool completely.
To serve, pour the lemonade into tall glasses with ice. Add a sprig of thyme and a grilled lemon slice. Serve immediately.
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.