Bring the water and sugar to the boil in a small saucepan over high heat. Stir in the rosemary and set aside to steep for 1 hour.
Place half of the lemon juice and half of the watermelon into a liquidiser. Sieve the rosemary syrup through a sieve into the liquidiser. Cover and puree until smooth. Sieve into a pitcher or a serving jug, then puree the remaining lemon juice and watermelon. Stir the lemonade before serving over ice.