If canning, prepare a water bath canner and jars before beginning. Canning is optional.
Wash and slice persimmons, removing tops/leaves. You should have around 11-12 cups of slices from 4 lbs fresh fruit.
Place persimmons in a deep, heavy bottomed stock pot or dutch oven.
Add lemon juice, but don't add sugar yet.
Turn on the stove to medium heat and cook the persimmons for about 15 minutes. Stir frequently to avoid scorching and mash with the fruit to encourage it to break apart.
After about 15 minutes of cooking, the fruit should have mostly fallen apart. Add the sugar and stir to dissolve.
Continue cooking the jam over medium heat for another 20 to 30 minutes, stirring frequently. The jam should thicken up nicely.
When the jam reaches your desired consistency, remove the pan from the heat.
Ladle the finished persimmon jam into prepared jars, leaving 1/4 inch headspace. Cap with 2 part lids.
If canning, load the jars into a water bath canner and turn the heat up to high to bring the canner to a full rolling boil. Once the water is boiling, start a timer and process the jars in a boiling water bath canner for 10 minutes, adjusting for altitude. Remove the jars and allow them to cool on a towel on the counter. After 12 to 24 hours, check seals and store any unsealed jars in the refrigerator for immediate use. Properly canned and sealed jars will maintain peak quality on the pantry shelf for 18 months, and keep much longer. Refrigerate after opening.