In a blender, combine the limes, water, sweetened condensed milk and rum, if using.
Blend on high speed for 15 seconds, or until the limes are puréed and the drink is frothy.
Using a fine-mesh strainer, carefully strain the lemonade into a large pitcher. Chill in the refrigerator until ready to serve and for up to 1 day.
Serve the Brazilian Lemonade over ice. Enjoy!