If canning, prepare a water bath canner, jars, and lids before beginning. Sterilize the jars since the processing time is under 10 minutes.
Wash the plums and cut them in half to remove the pits. Chop the plums coarsely, leaving the skins on.
Combine the chopped plums, water, sugar, and lemon juice in a large, heavy-bottomed pot. Stir to distribute the sugar and bring the mixture slowly to a boil over medium heat, stirring occasionally until the sugar dissolves.
Once boiling, increase the heat and cook rapidly, stirring constantly to prevent sticking or burning. The plums will break down as they cook and the mixture will thicken.
Cook until the jam reaches gel point, about 220°F at sea level (8°F above the boiling point of water). You can also test for set using the cold plate method: drop a spoonful onto a chilled plate, wait 30 seconds, and push it with your finger. If it wrinkles, it's ready.
Remove the pot from the heat and skim off any foam if desired. Ladle the hot jam into prepared jars, leaving 1/4 inch headspace. Wipe the rims clean, apply lids and bands, and tighten to fingertip tight.
Process in a boiling water bath for 5 minutes at elevations up to 1,000 feet. Increase to 10 minutes at 1,001 to 6,000 feet, or 15 minutes above 6,000 feet.
Remove jars from the canner and let them cool undisturbed for 12 to 24 hours. Check seals before storing. Properly sealed jars keep at room temperature for 12 to 18 months.