Wash the peaches well in cold water, then cut them into wedges, discarding the pits, and place the wedges in a mixing bowl. (You can also peel them if you like, though I don't—see Notes below.) Sprinkle the peach wedges with the sugar and the juice of half a lemon. Mix gently with a rubber spatula to avoid bruising—ripe peaches are quite delicate—and allow the peaches to rest for about 15 minutes or so, or until the sugar has dissolved and the fruit has softened a bit.