Combine sugar and water in a small saucepan; bring to a boil. Cook 1 minute or until sugar dissolves. Cool sugar syrup completely.
Cook lemon verbena leaves in boiling water 1 minute. Drain and plunge into ice water; drain.
Combine sugar syrup and verbena leaves in a blender; process until smooth. Cover and chill overnight. Strain sugar syrup through a fine sieve into a bowl. Place 2/3 cup ice into each of 6 tall glasses; add 1 cup brewed tea and 2 tablespoons sugar syrup to each serving, stirring to combine. Garnish with mint leaves and lemon wedges, if desired.
Blanching the herb leaves brightens their color so the syrup will stay green. Avoid using a strongly flavored tea, such as Earl Grey, as it will overpower the taste of the syrup.