Lightly mash the lemon grass with the dull side of a knife and then slice thinly. Slice ginger root. Add the lemon grass and ginger to a medium sized pan with water and bring to a boil. Allow to cook 10 minutes and then remove from the heat. Stir in the honey and allow to sit covered for 20 minutes. Strain the lemon-grass ginger syrup. Portion the black tea and lime juice into the glasses and top off with the lemon-grass ginger syrup. Serve with ice.