Lemon Fig Sauce

In the bowl of a food processor fitted with the metal blade, process the lemon halves (including rind) until finely chopped, about 15 seconds. Transfer to a small saucepan. Add the figs, sugar, and gingerroot. Heat the mixture over medium-high heat until simmering, stirring occasionally. Simmer until thickened, about 20 minutes. Remove from heat, and cool completely before serving. Store refrigerated in an airtight container up to 1 week.