In a saucepan, combine pomegranate juice, sugar (or sweetener), and freshly squeezed lemon juice.
Stir over medium heat until the sugar fully dissolves.
Bring the mixture to a gentle simmer, then reduce the heat to low and simmer for 10-15 minutes to thicken.
Allow the grenadine to cool to room temperature.
Strain the syrup to remove any pulp.
Optionally, add a tablespoon of vodka to extend the shelf life.
Transfer the grenadine to a clean, airtight bottle and store in the refrigerator.