Combine the sugar, water, lime juice and lime zest in a large pan and place over a medium heat. Cook until all the sugar has dissolved. Allow to cool.
Place the mango chunks into a food processor with half of the cooled syrup, and blend until smooth. Pour into a shallow container, and freeze in the freezer for two hours. Remove the sorbet from the freezer at regular intervals to stir it until the mixture reaches the consistency of sorbet.
Meanwhile, arrange the paw paw in a shallow dish. Pour over the remaining cooled syrup and allow it to infuse for at least one hour.
Serve the marinated paw paw with a scoop of the mango sorbet.