Toss together the sliced fruit and sugar in a large bowl and let stand at room temperature for 3 hours or cover and refrigerate overnight.

Place a large colander in a 12-inch skillet and pour the fruit and juice through. Allow to drain for 1 hour. Remove the colander with the fruit to a bowl to collect any additional juices and bring the syrup in the skillet to a boil over high heat. Cook until reduced by half and very syrupy, about 7 minutes.

Add the fruit and any accumulated juices and cook, stirring, for 10 minutes. The fruit will soften and the skin will come off and tint the syrup. Process half of the contents of the skillet in a food processor until smooth. The puree will thicken the jam so that the fruit does not need to be cooked further. Return it to the skillet. Add the honey and lemon juice, stir to combine, and taste for additional lemon juice.

Bring the mixture back to a simmer and ladle into hot sterilized jars, wipe the rims clean with a damp towel, and seal with new lids and metal rings. Process in a hot-water bath for 10 minutes. Remove, cool, check seals, label, and store.