Combine pomegranate juice, sugar, and lemon juice in a medium saucepan. Bring to a boil over medium-high heat, stirring until sugar dissolves, about 5 minutes.

Reduce heat to medium-low and simmer, stirring occasionally, until the syrup thickens slightly and coats the back of a spoon, 10 to 15 minutes.

Remove from heat and let cool for 10 minutes. Pour through a fine-mesh strainer into a clean bottle or jar. Cool completely, then seal and refrigerate.