Working in batches, puree cantaloupe in a blender until smooth. Set a fine-mesh sieve over a large bowl; line sieve with cheesecloth. Strain puree 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.