Pound the lemongrass stalk with the back of a knife to break the cell walls. Cut the stalk in half or thirds lengthwise to fit comfortably in a small saucepan.
Bring a small saucepan with a little over 2 cups water to a simmer, and add the lemongrass. Remove it from the heat and allow it to steep, 10 to 15 minutes. Strain and chill the lemongrass water completely. Discard the lemongrass solids.
In a blender, combine the coconut water, lychees, lemongrass water and salt and let it go until the concoction is smooth; depending on how large your blender is, you might have to do this in batches. Taste for seasoning, chill and serve; you can strain it if you don't like pulp.
*Lemongrass is available at Asian markets and specialty produce stores. **Lychee is available in the international aisle of some supermarkets, and at Asian markets.