Place the diced pineapple, water, sugar, and freshly squeezed lemon juice into a blender. Blend on high speed for about one minute until smooth and fully liquefied.

Pour the mixture through a fine mesh strainer into a large pitcher to remove any fibrous solids. Use a spoon or spatula to press down on the pulp, extracting as much juice as possible. Discard the remaining solids after straining.

Refrigerate the juice until cold, or until ready to serve. Just before serving, stir in the mineral or soda water for a bubbly finish. Add ice cubes to each glass if desired, and serve chilled.