Cut the watermelon into small cubes using a sharp knife and cutting board to facilitate blending.
Place the watermelon cubes into a blender and blend on high speed until smooth and frothy, about 30-45 seconds. The mixture should be bright pink and uniform in texture.
Pour the blended watermelon through a fine mesh strainer into a pitcher to remove pulp and seeds, pressing gently with a spatula to extract as much liquid as possible.
Add fresh lemon juice and sugar to the strained watermelon juice in the pitcher. Stir with a spoon until the sugar dissolves completely, observing the liquid turn slightly paler and frothy at the surface.
Pour in the cold water and stir gently to combine. The beverage should appear uniformly pink with a light froth forming on top. Serve immediately over ice if desired.
