Wash the plums (do not peel or remove the pits) and place in a large, heavy-bottomed pot. Add enough water to barely cover the plums, then bring to a boil over medium-high heat. Lower the heat to maintain a strong simmer, and cook until the fruit is very tender, 20–25 minutes. Remove from the heat, and let cool slightly. In a large strainer set over a large, heat-resistant bowl, strain the plums without pressing on the fruit or attempting to force the pulp through the strainer. Reserve the plum juice for another use. Pass the plums through the 3-millimeter plate of a food mill, removing the pits manually so as not to jam up the mill. Measure the pulp (you should have about 2½ cups or 1¼ pounds). Stir in the sugar, adding more as needed to maintain a ratio of 6 parts sugar to 10 parts fruit. Add the lemon juice, cover, and refrigerate for at least 8 hours and up to 1 day.
When ready to cook, place a small, heat-resistant plate in the freezer.
Transfer the plum mixture to a large, nonreactive pot. Bring to a boil over high heat, then lower the heat to maintain a very low simmer. Cook, stirring frequently to prevent hot spots and scorching, until very thick and glossy, about 1 hour 15 minutes. (Use a candy thermometer to ensure the mixture never exceeds 221°F.) You should be able to run a wooden spoon through the mixture, and it will briefly stay apart.
Retrieve the plate from the freezer and place a small drop of the plum mixture on the surface. If it starts to set and form a skin after a minute, the preserves are ready. If it remains runny, return the plate to the freezer and cook the plum mixture a few minutes more before testing again.
Remove the plum mixture from the heat. Ladle carefully into sterilized jars, then clean the rims and sides with a kitchen towel and seal firmly with lids. Check for air bubbles, and if necessary, tap the jars gently on the towel to work any bubbles upwards and out. Follow recommended water bath canning procedures to jar, or let cool completely and refrigerate for up to 2 weeks or freeze for up to 3 months.