Wash the pomegranates. Roll them around until they soften, then break up the pomegranates under water to keep juice from spurting. Give a good bang with the back of the knife to loosen the seeds of each section.
To squeeze out the juice: Wrap a handful of seeds in cheesecloth, then use your hands to squeeze into a bowl to obtain the rich, shiny liquid. Repeat wit the remaining seeds. (Do not use a juicer. Pomegranate juice stains are difficult to remove, and the bitter, tannic white part of the fruit gets mixed in and mars the flavor).
Place pomegranate juice, sugar and lemon juice in an enameled saucepan and slowly reduce by boiling to 2 cups. Cool, bottle, and keep refrigerated.