Cut an X in the rounded end of each peach. Bring a saucepan full of water to a boil over high heat. Have ready a bowl of ice water. Add peaches a few at a time to the boiling water and blanch 30 seconds, then transfer to the ice water to stop the cooking. When cool, lift out and peel. The skin should peel back easily from the X.
Cut peaches into wedges about 1/2 inch thick, then cut each wedge in half crosswise. Transfer to a large bowl, add sugar and lemon juice and stir well. Let stand several hours or overnight, stirring two or three times, until sugar dissolves and mixture no longer tastes grainy.
Transfer to a large pot, bring to a simmer over moderately high heat and simmer, skimming any white foam that collects on the surface, until peaches are tender and syrup thickens slightly, 25 to 30 minutes. Transfer to a large bowl, cover and let rest overnight to "plump" the fruit again.
Drain the fruit in a sieve set over a bowl. Taste the syrup and add more lemon juice if it seems too sweet. Return the syrup to a pot and cook over moderately high heat until it reaches 220F 105C). Or test for jamlike consistency by spooning a little onto a chilled saucer, then returning the saucer to the freezer for a couple of minutes to cool the syrup quickly. It should firm to a soft jelly consistency.
Return the peaches and any collected juices to the pot and cook a couple of minutes more, until mixture returns to 220 F (105 C). It will seem thin.
Remove from heat and let stand 5 minutes, then spoon into clean, hot jars to within 1/2 inch from the top. Wipe rim clean with a towel dipped in hot water. Place lids and rings on jars and seal tightly.
Cool and refrigerate for up to 3 months. Or, for longer storage, place just-filled jars in boiling water to cover by 1 inch and boil 15 minutes for half-pint jars, 20 minutes for pint jars.
Transfer with tongs to a rack to cool; lids should form a seal. Sealed jars may be stored in a pantry for up to a year.