In a large pot, combine rhubarb, sugar, and water. Bring the mixture to a boil over medium-high heat. Once it starts boiling, lower the heat and let it simmer until the rhubarb is soft, about 20-25 minutes.
Strain the mixture through a fine mesh sieve into a bowl, pressing the rhubarb with a spoon to extract all the juice. Transfer the liquid to an airtight container and refrigerate until cool.
In a large pitcher, mix the cooled rhubarb syrup, lemon juice, and cold water. Stir well.
Add ice cubes to glasses, pour in the lemonade, and enjoy!