Place four dried black limes in a large mortar or molcajete.
With a few firm hits with the pestle, crack the limes open. You can stop pounding when each lime has opened up - need not grind to powder.
Transfer the cracked dried limes into a pan, and add 1.5 liters of water.
Bring to a boil, then simmer for 15 minutes. The bubbling water would turn black as the dried limes release their juices and flavor.
Switch off the heat, and stir in the sugar till it dissolves.
Let the pan cool naturally to room temperature. Strain the drink into a clean bottle or jug with a tight-fitting lid, and discard the cooked black lime bits. Transfer the drink to the refrigerator to chill.
Dried black lime cold drink is ready to serve.