First make the ginger-lemon sauce. With a small knife, peel off the hard outer skin of the ginger, then grate the flesh finely, discarding any stringy threads.
Place the grated ginger, sugar and 1 tablespoon of lemon juice in a saucepan with 250 ml of water and bring the mixture to the boil, stirring frequently to dissolve the sugar before it boils. Reduce the heat to low and simmer for 20 minutes, or until the sauce has thickened enough to coat a spoon lightly. Taste it and add extra lemon juice if desired.
Transfer the sauce to a bowl to cool for 30 minutes, then place the sauce and the melon in the refrigerator, separately, to chill overnight.
When you are ready to serve, cut the melon in half lengthways and scoop out the seeds. Cut each half into four wedges, then trim off the rind. Put a slice of melon on each plate, pour the chilled sauce over it and garnish with a sprig of mint.
Variation: the ginger-lemon sauce can be used to accompany ice cream.