And I found a clever lady in New Zealand called Emma who has been preaching the same ideas on her blog Craving Fresh. Here are some of her photos, cause a visual aid is always helpful.
Photo source: Craving Fresh - juice
And while you're at it, why not zest your lemons/limes/oranges and store in a plastic container or ziplock bag in the freezer.
Photo source: Craving Fresh - zest