Squeeze the lemons until you get ¼ cup lemon juice. Add to a large measuring cup.
Whisk the sugar in with the lemon juice until incorporated with a small whisk, roughly 1 to 2 minutes.
Pour the lemon mixture into a blender with the cold water and ice cream.
Pulse or blend 1 to 2 minutes, or until you reach a thick milkshake consistency.
Divide into two glasses and enjoy!
