Cut 2 limes into thin slices. Squeeze 1 lime. Pluck the mint leaves from the stems. Bring the lime juice, 2/3 of the mint leaves, sugar and 125 ml water to the boil in a small saucepan and simmer for 5 minutes. Let the brew cool down.
Halve the melons and remove the stones with a spoon. Remove or dice the pulp with a ball cutter.
Put the melons, lime slices and the remaining mint leaves in a large glass vessel. Pour the lime and mint stock through a sieve over the melon balls and marinate for 30 minutes. Add the ice cubes and fill up with the orange lemonade.