Place the cantaloupe, 1 1/2 cups of the water, the lime juice, and measured sugar in a blender and blend on high speed until smooth, about 20 seconds.
Strain through a fine-mesh strainer set over a large pitcher or bowl, using a ladle or wooden spoon to press down on the solids (you should have about 2 cups of liquid). Discard the solids.
Add the remaining 1 1/2 cups water and stir to combine. Taste and add additional sugar as needed. Refrigerate until cold, at least 1 hour. Serve over ice.