Dissolve the sugar in 1 cup water and bring to a boil in a small saucepan. Reduce the heat to low and cook until the mixture turns syrupy, about 5 minutes. Remove from the heat. Place the tea bags in the saucepan and let the mixture come to room temperature. Refrigerate until cold, about 2 hours. (Syrup will keep up to one month stored in the refrigerator in a container with a tight fitting lid.)
Spoon 3 tablespoons of the cold Earl Grey simple syrup into each Champagne flute. Garnish with a thin slice of lemon.