Working in batches, purée cantaloupe in a blender until smooth.
Set a fine-mesh sieve over a large bowl; line sieve with cheesecloth. Strain purée into bowl; gather cheesecloth into a bundle and squeeze any remaining juice into bowl. Repeat process with fresh cheesecloth, straining into a large pitcher (you should have about 5 cups juice).
Add lemon juice, basil, and 2 cups cold water to pitcher.
Let steep at room temperature for 1–2 hours. Fill glasses with ice. Divide agua fresca among glasses.
