Measure out the fresh lemon juice and pour it into a blender.
Add the granulated sugar to the blender with the lemon juice.
Pour in the cold water or add ice to the mixture.
Secure the lid on the blender and blend on high speed until the mixture is well combined and appears frosty, about 30 seconds.
Check the consistency—if it's too runny, add more ice and blend briefly again until you reach the desired slushy texture.
Pour the bright, icy lemonade into glasses, and enjoy immediately for the best texture.