Combine the chopped peaches and water in a large, heavy-bottomed pot or Dutch oven. Bring to a simmer over medium heat.

Cook the peaches gently for about 15-20 minutes, stirring occasionally, until they begin to soften significantly. Mash lightly with a potato masher if you prefer a smoother consistency.

Stir in the granulated sugar until completely dissolved. Bring the mixture to a full, rolling boil that cannot be stirred down. This is crucial for pectin activation.

Add the fresh lemon juice. Continue to boil vigorously, stirring constantly to prevent scorching, for 25 to 35 minutes. Monitor the temperature; the setting point is typically reached around 220°F (104°C).

Test for the set: Place a small spoonful of the hot marmalade on a chilled plate. Return it to the freezer for 1 minute. Push the edge of the marmalade with your finger; if it wrinkles, the set is achieved.

Remove from heat, skim off any foam from the surface, and carefully ladle the hot marmalade into sterilized half-pint jars, leaving 1/4 inch headspace.

Wipe rims clean, seal with lids and bands, and process in a boiling water bath canner for 10 minutes for shelf stability, adjusting time for altitude.