In a large pot, combine the fruit with the water and cook over moderate heat, stirring occasionally, just until the fruit softens, about 15 minutes. Set a food mill over a heatproof bowl and pass the fruit through the mill to remove any skins.

Return the pureed fruit to the pot. Add the sugar and lemon juice and bring to a rapid boil. Reduce the heat to low and cook, stirring frequently to prevent scorching, until the puree is very thick and reduced to 4 to 5 cups, 1 hour and 15 minutes to 1 hour and 30 minutes. Spoon the fruit butter into 1/2-pint jars and tap gently to release any air bubbles. Let cool, then cover and refrigerate for up to 4 months or freeze for up to 6 months.