Place into a blender and pulse for 10 seconds or so, until the lemon is properly chopped up. Take care not to over mix, especially in a high powered blender, as the lemon pith can make the lemonade bitter. You just want to incorporate the lemon pieces into the water.
Leave the lemonade for a few minutes while you slice the fruit into pieces.
Fill your ice lolly moulds with fruit. Pack as much as you can get in there.
Using a wire sieve or a nut milk bag, strain the lemonade.
Taste test. Add more sugar if you feel it needs it, or keep as is if you want a proper lemony kick to your ice lollies.
Pour lemonade into each of the ice lolly moulds. Insert a wooden lolly stick (the fruit will keep it in place) and place into a freezer for 6 hours.