Remove the crown and greens from the beets and reserve for another use. Trim any unattractive bits of root and any soft spots, but leave beets otherwise unpeeled.
Cut each beet into quarters or eighths, but make sure the pieces are at least 1 inch thick. Scrub and quarter the lemons. Place the ginger, coriander, bay leaves, allspice berries, juniper berries, and salt (if using) into a 1-gallon jar, add the beets and unsqueezed lemon wedges, and pour in the filtered water to fill to 2 inches below the rim. Place the lid on your jar but don’t fully tighten it so that carbon dioxide (a natural product of the fermentation process) can escape.
Leave it to ferment at room temperature for 7 to 10 days. Give the jar a little swirl every day to prevent surface yeasts from forming. Once you’re happy with the acidity and flavor, strain the liquid into a clean jar, cover and chill before drinking.