Rinse lemon grass, cut into 2-inch lengths, and crush with the flat side of a large knife.
In a 2-quart pan, bring 5 cups water, sugar, ginger, and lemon grass to a boil. Take off heat and add green tea bags; let steep about 4 minutes or until flavor is as strong as you like. Discard tea bags; let tea cool, about 30 minutes.
Pour through a fine strainer into a pitcher. Cover and chill until cold, at least 2 hours (see Notes). Pour into tall glasses filled with ice.