In a small saucepan over medium heat, add 1-cup pomegranate juice, sugar and lemon juice. Cook until the sugar has dissolved, stirring occasionally. When the sugar has dissolved, reduce heat to medium-low and cook until the syrup has reduced to 1/3 cup, about 45 minutes, stirring occasionally. The syrup should be dark and slightly thick. It would get thicker when cool. Remove from heat and let it cool for 30 minutes. Transfer to an airtight container. Let it cool completely before placing in the fridge.