Place the pomegranate juice, sugar, and lemon juice in a 4-quart saucepan set over medium heat. Bring to boil over medium-high heat. Reduce the heat to medium-low and cook, stirring occasionally, until reduced to 3/4 cup, approximately 40 minutes. 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.