Note that in Brazil this recipe is called “lemonade”, but it does use limes, not lemons! Rinse the whole limes thoroughly under water and cut the ends off of each lime. Cut each lime in half and slice each half into 1/2 inch slices. Place the limes in the blender. Add the cold water to the blender, cover, and blend for about 15 seconds, so that the limes are broken down, but not fully blended.
Place a sieve over a large bowl and slowly pour the mixture into the sieve, letting the liquid strain through into the bowl. Using a spoon, press down on the lime mixture to squeeze out any remaining liquid.
Pour the liquid back into the blender and add a ½ cup of the sweetened condensed milk. Blend for another 15 seconds, until the mixture is frothy. Taste for sweetness and if you prefer a sweeter taste, add more condensed milk and blend for another 10 seconds.
Pour the mixture into glasses over ice and enjoy!