Put limes, sugar, sweetened condensed milk and 4 cups of water in a blender. Blend at the lowest speed until limes are fairly shredded, about 2 minutes. Pour through a strainer over a large container, using a spoon to press out all the liquid; discard limes.

Put the liquid back into the blender. Add the remaining 3 cups of water and blend on low speed just until mixed.

Serve over ice.