Begin the preceding night by squeezing the lemons into a strainer formed by placing a coffee filter in a strainer. Strain the lemon juice into a small bowl containing the cold water - this is a very slow drop-by-drop process.
Add the sugar the next morning.
Mix very well with a wooden spoon until the sugar is completely dissolved.
Pour into a tin or aluminum pan.
Place the pan in the freezer.
Let rest for about 5 hours, breaking up the solid layer of ice which forms at least once every hour.
Remove the pan from the freezer.
Cut the ice into pieces with a knife.
Place the ice pieces in an ice crusher (or into a blender running at low speed).
The ice should form a smooth consistent texture of imperceptible grains (almost like ice cream - no large grains or chunks).