Add the sugar and one cup of water to a sauce pan. Over medium heat, simmer and stir until the sugar has dissolved.
Add 1/2 cup of the pomegranate seeds to the sauce pan. (Save the rest for garnish.)
Using a fork or a masher, mash the pomegranate seeds and stir into the sugar and water mixture. Allow this mixture to cool.
Once cooled, strain the mixture through cheese cloth or through a very fine mesh sieve. Discard the pulp, but save the juice. (If you prefer, you do not need to strain at all. You can leave the pulp in, but it will make for a cloudier drink.)
Add five cups of water to a pitcher. Pour in the pomegranate juice and add the lemon juice. Stir to combine.
Add some of the leftover pomegranate seeds and some ice to the pitcher. Stir to combine and serve immediately.