Wash limes thoroughly by, scrubbing the skin with hand or dish soap to remove any pesticides or wax. Slice off the ends of each lime, then cut them into ⅛ths.
In a blender, combine half of the water, half of the sugar, and half of the limes, then pulse 5-7 times. Pour through a fine-mesh strainer into a pitcher, pressing the lime pulp with a spoon to help release juices, then discarding the remaining skins and pulp. Repeat with the other half of the water, sugar, and limes.
Stir the sweetened condensed milk into the limeade and serve with lots of ice and thin slices of lime for garnish. If the drink tastes bitter at all, you can add a little extra sweetened condensed milk or sugar as needed.