Prepare a water bath canner, jars, and lids, with the canner water at about 180 degrees F.
Wash the quince, core it the way you would an apple, and cut it into 1/2 to 1 inch pieces. Peel it if you like.
Put the quince in a saucepan with a bit of water. Simmer and stir until it falls apart and turns from white to rosy pink, about 30 to 45 minutes, adding more water if the pan starts to run dry. Don't drain off the cooking liquid.
Stir to break up the quince, or use an immersion blender if you left the peels on.
Add the lemon juice and sugar, to taste, and stir until the sugar dissolves.
Keep cooking, stirring often, until the jam thickens and reaches the gel stage.
Ladle the hot jam into hot jars, leaving 1/4 inch headspace. Wipe the rims and apply the lids fingertip tight.
Process half pints in a boiling water bath canner for 10 minutes, adjusting for altitude (see notes).
Turn off the heat, take the lid off the canner, and let the jars sit in the water for 5 minutes before lifting them out onto a towel.
Cool 12 to 24 hours, then check the seals.