If using lemon, squeeze out all the juice into a bowl. If using lime, and if they are thin-skinned, you can quarter them put them into the blender with the skin on. Try it! The skin gives it an interesting flavor.
To the blender add the lemon juice if using, or the quartered lime pieces.
Add the ginger, mint leaves, honey or raw sugar and a quarter glass of slightly warm water and run until fully blended.
Strain this juice into a pitcher. Add the 2 glasses cool water.
Taste and adjust the honey or sugar to your taste.