Cut the lemons and lime into wedges (fourths or eighths depending on the size of the lemon). Place in a blender with the water and the sugar. Blend on high speed for a minute or until the lemons have been broken down and the water looks like lemonade. Let the mixture sit for a few minutes so the broken down pieces of lemon rise to the top of the blender.
Pour the lemonade through a metal strainer over a large pitcher. You may need to do this in batches so that you can empty the lemon pieces out of the strainer. KEEP the lemon pieces! Use the mixture for muffins, fruit desserts, jam, pasta, or just cleaning your garbage disposal in the sink.
Add the sweetened condensed milk to the lemonade in the pitcher. Stir to combine or pulse quickly through the blender. The lemonade will separate after about 15 minutes, so just keep a wooden spoon handy and give it a quick stir before serving.