Place the pomegranate juice, sugar, and lemon juice in a 4-quart saucepan set over medium heat. Cook, stirring occasionally, until the sugar has completely dissolved. Once the sugar has dissolved, reduce the heat to medium-low, and cook until the mixture has reduced to 1 1/2 cups, approximately 50 minutes. It should be the consistency of syrup. Remove from the heat and allow to cool in the saucepan for 30 minutes. Transfer to a glass jar and allow to cool completely before covering and storing in the refrigerator for up to 6 months.