In a saucepan, combine the water, lemongrass, ginger, and sugar. Bring to a boil and then reduce to a simmer. Simmer for 15 minutes. Remove from the heat and allow to cool until it reaches 135°F. Remove the lemongrass and ginger and place both in a large sealable bowl.
Using a tea infuser, add the gyokuro tea leaves and about ½ of the cooled water. Let it infuse for 90 seconds. Pour into the sealable bowl that has the lemongrass and ginger. Add the remaining water into the infuser and transfer to the bowl quickly afterward. Place in the refrigerator and allow to cool for at least 1 hour.
To serve, in a cocktail shaker add the ice, lime juice, brewed tea, and whiskey. Shake for 10 seconds. Fill a glass half way with ice. Pour the mixture from the shaker (do not include the ice). Add the ginger beer to the glass and stir lightly.
