Add the mango chunks to a blender with 1 cup of the cold water. Blend on high speed for 45-60 seconds until completely smooth with no visible chunks remaining.
Pour the mango puree into a large pitcher. Add the freshly squeezed lemon juice and sugar, stirring well until the sugar dissolves completely.
Add the remaining 3 cups of cold water to the pitcher and stir to combine. Taste and adjust sweetness by adding more sugar if desired, keeping in mind the mango's natural sweetness.
Gently muddle the fresh mint leaves with a wooden spoon for 5-10 seconds to release their oils, then add them to the pitcher. Stir gently to distribute the mint throughout.
Refrigerate for at least 30 minutes to allow the flavors to meld and the mint to infuse. For best results, chill for 1-2 hours.
Before serving, give the lemonade a good stir. Fill glasses with ice cubes and pour the lemonade over top, straining out the mint leaves if desired.
Garnish each glass with a lemon slice and a fresh mint sprig. Serve immediately while cold and refreshing.