Place the cubed watermelon flesh into the blender.
Blend on high speed until the mixture is smooth and frothy, about 30 seconds. The puree should be bright pink with no large chunks.
Set a strainer over a large jug or pitcher and pour the blended watermelon through it, pressing gently with a spoon to extract as much liquid as possible. Discard the pulp or save for another use.
Add the freshly squeezed lemon juice and sugar or honey (if using) to the strained watermelon juice. Stir well until the sweetener dissolves completely.
Pour in the cold water and give the mixture a final stir. Taste and adjust sweetness or acidity as needed.
Serve immediately over ice or refrigerate until chilled. The lemonade will have a vibrant pink color with a refreshing aroma of summer fruit.
