Add the diced cucumber and peeled lemons together with the mint leaves and agave syrup to a powerful blender or food processor. Add the water and blend until smooth to your liking. ( If using a food processor you might want to strain it at this point. If using a Vitamix there won't be any need for straining).Taste and adjust sweetness with more syrup or nectar.
Transfer the lemonade to a pitcher with the reserved cucumber, lemon slices and mint sprigs. Serve over ice.
Add 1/4 cup of chia seeds to the lemonade to boost up the nutritional value.
If using a powerful blender like a Vitamix you won't need to strain the lemonade.