Cut the watermelon into 2 then slice into manageable segments, remove pips and dice the watermelon into cubes.
Blend watermelon in a power blender and pass the juice through a tiny mesh/sieve. You can eat the pulp if you wish or add a bit back to the watermelon juice. Transfer the watermelon juice into a clean large bowl or pitcher.
Place a small saucepan on medium heat, add sugar and water to make syrup.
Add the lemon juice to the watermelon juice and stir in the sugar syrup, add some ice and finish it off with some mint leaves.
Serve immediately over ice or leave to chill in the fridge before serving
Notes
If watermelon juice becomes cloudy after sieving, there is a probability that you haven't sieved it through a tiny mesh and some pulp has escaped into the juice. There is nothing to worry about as it doesn't affect the taste. If you want, you can sieve it again but this time using the tiniest hole sieve you may have.
Watermelon will separate and sink at the bottom if left to sit for a while. Nothing to fret about, just give it a quick stir and drink up.