Cut pomegranates in half, and extract juice from seeds with a juicer or reamer. Strain through a fine sieve into a large bowl, discarding pulp. You should have about 3 1/3 cups juice.
In a small saucepan, bring 2 cups water and sugar to a boil. Reduce to a simmer, and stir until sugar dissolves. Add pomegranate juice, mint, and lemon juice. Cover; let steep 30 minutes. Remove and discard mint; let cool completely.
Transfer to an airtight container; chill until ready to serve, up to 2 days.