In a large bowl or pitcher, combine water and tea. Let sit at room temperature until cool.
Tear mint into pieces and add to pitcher. Using only the bottom 2-inches of lemongrass stalk, cut into chunks and bruise with the back of your knife. Add to pitcher along with 2 cups cold water. Refrigerate at least 4 hours or overnight.
To serve, strain through cheesecloth or a fine sieve and pour over ice in tall iced tea glasses. Garnish with additional sprigs of mint and lemongrass if desired.