In a small saucepan, bring cherry juice, about 1 cup, to a boil over moderate high heat. Whisk in sugar and cornstarch in lemon juice to create a slurry. To juice, add slurry and let thicken 1 to 2 minutes. Add cherries and stir 1 minute longer. Remove from heat. Ladle cherries in cherry sauce on dessert plates and top with ice cream. Slivered almonds and amaretti cookies make a nice finishing touch.