Wash and scrub the lime well. Cut off the ends and discard them. Cut the limes into 8 pieces and place half of them into a blender. (You're going to be working in 2 batches.)
Add half of the water and sugar to the limes. Cover and pulse the blender for about 10 seconds.
Pour the lime mixture through a mesh strainer into a pitcher. Repeat with the remaining limes, water, and sugar.
Pour the sweetened condensed milk into the pitcher and stir until well combined. Check the sweetness and add more condensed milk if desired.
Chill in the fridge and serve over ice when you are ready to enjoy.