Peel and rough chop the peaches.
I love my serrated vegetable peeler for this job. The fine teeth make quick work of the soft peach skin. Add the peaches to a heavy pot along with the water and sugar. Heat on medium, stirring to dissolve the sugar. When the mixture comes to a boil, lower the heat slightly and cook for about 20 minutes until the peaches are completely tender. Stir occasionally. Add the lemon juice to the peaches, and then, working in batches, puree the fruit until it is completely smooth. Don't rush this step, let the processor or blender run long enough to get all of the lumps. At this point I strain the puree through a mesh strainer just to make sure it is completely smooth. Push it firmly with the back of a spoon to get all the puree through. Discard any lumps. If your puree is smooth enough, you can skip this step. Put the puree back into the pan and bring back up to a boil. Lower the heat and cook gently until it is greatly reduced and thickened. This will take about 25-30 minutes or so, depending on the size of your pan. Stir very frequently during this step so the fruit doesn't scorch. I like to use a splatter screen because it does splatter.
the longer you cook the peach puree, the thicker the butter will be. You know it's ready when it starts to darken slightly, and your stirring starts to leave trails in the mixture. Test it by dipping a spoon in, and then run your finger down the spoon, if the butter doesn't fill in the strip, it's ready. Ladle the hot peach butter into a clean jar or jars and let cool before capping and refrigerating. The peach butter will thicken as it cools. Consume within a couple of weeks. You can also freeze the butter for up to 6 months, just put the cooled butter into a freezer safe container, leaving 1/2 inch at the top to allow for expansion.