Place whole tomatoes in a large glass mixing bowl, and sprinkle with sugar. Cover and refrigerate overnight.
Drain mixture, reserving tomatoes and liquid. Place liquid and any undissolved sugar in a flat-bottomed kettle; stir well. Bring to a rolling boil; boil, stirring occasionally, until mixture registers 230° on a candy thermometer or until mixture thickens.
Scrape outer surface of lemons with blade of a knife to release citrus oils. Cut lemons into thin slices, discarding seeds. Add lemon slices, tomatoes, gingerroot, cinnamon, and salt to syrup mixture, mixing well. Bring to a boil; boil, stirring frequently, until tomatoes become translucent. Discard gingerroot and cinnamon.
Quickly ladle preserves into hot sterilized jars, leaving 1/4- inch headspace. Cover at once with metal lids, and screw bands tight. Process preserves in boiling-water bath 15 minutes.