Place the persimmons in a food processor and grind until smooth.
Place the persimmon puree, sugar, lemon juice and zest in a small saucepan. Bring to a boil, then reduce the heat to low and simmer for about 15-20 minutes, stirring occasionally.
Notes
1)This is good in the fridge for a week. 2) You can freeze this in freezer bags or jars.3) If you feel it needs to be thickened you can dissolve 1 Tablespoon of cornstarch into 2 Tablespoons of water, then pour the mixture into the jam. If you feel it needs to be thinned out, you can add more lemon juice or just a bit of water and whisk.