Drain litchis from syrup into heavy small saucepan. Place litchis in medium bowl. Add orange slices to syrup and boil until syrup thickens, about 10 minutes. Remove orange slices from syrup. Pour syrup over litchis. Mix in Cointreau and ginger. (Can be prepared 2 days ahead. Cover and refrigerate.) Scoop ice cream into bowls. Spoon litchis and syrup over.