Rinse and drain cranberries. Remove and discard any bruised or soft ones. Gently pat berries dry.
With a vegetable peeler, pare all the yellow peel (not the white pith) from lemon in thin strips; coarsely chop. Save lemon for other uses.
In a food processor, whirl cranberries, lemon peel, sugar, crystallized ginger, and ground ginger just until finely chopped. Cover and chill at least 4 hours.