In a medium saucepan over high heat, combine the coconut with the water and bring to a boil. Reduce the heat to an active simmer, about medium-low, and let the coconut cook for 10 minutes. Cover and remove the pan from the heat.
On a cutting board, trim off the long, dry stalks from the lemongrass plus the root end, leaving the thicker bulb intact. (On most stalks this will be about 6 to 8 inches [15 to 20 cm] long.) Using a rolling pin, kitchen mallet, or the broad side of a cleaver, smash the bulb once or twice so that the insides are exposed but the bulb is still more or less in one piece. Add the smashed lemongrass to the saucepan and let the mixture steep,
covered, for 30 minutes.
Remove the lemongrass bulb from the pan. Working in batches, transfer the coconut and steeping liquid to a high-speed blender and blend for 1 to 2 minutes, until very smooth.
Set a fine-mesh strainer over a pitcher and strain the mixture, pressing gently on the coconut solids to extract as much liquid as possible. Add the sugar and salt and stir until dissolved.
Chill the tea for at least 3 hours. Serve over ice.
