Disolve sugar into water and chill until ready to use.
Wash limes thoroughly...using soap. Cut limes into 8ths.
Place half of the limes in the blender with half of the water. Pulse 5 times. Place a fine-mesh strainer over a pitcher and pour the blended mixture through the strainer. Use a spoon to press any remain liquid into the pitcher. Discard the limes. Repeat with remaining limes and sugar water.
Add sweetened condensed milk. Taste, and add more if needed.
Serve immediately over ice.