Wash the apricots under cold running water and drain well. Halve, pit and then coarsely chop the fruit. No need to peel them—the skins dissolve during cooking and enhance the flavor.
In a large stainless steel saucepan, combine the apricots and water. Bring to a boil over medium-high heat. Reduce heat and simmer gently, stirring occasionally, for about 20 minutes, or until the apricots are very soft.
Use an immersion blender directly in the pot to puree the mixture until smooth, or transfer in batches to a food mill or food processor. You should have about 6 cups of apricot puree at this stage.
Return the puree to the pot (or transfer to a crockpot if using that method). Add the sugar and lemon juice, stirring until the sugar dissolves completely.
Bring the mixture to a boil over medium-high heat, then reduce to the lowest heat and simmer uncovered, stirring frequently, until the butter thickens and holds its shape on a spoon. This takes 1 to 2 hours on the stovetop, usually closer to 1½ hours. Stir often to prevent scorching, especially toward the end.
Crockpot option: Cook on high for 3 to 4 hours, uncovered, until thick. Stir occasionally, but it’s less prone to burning in a slow cooker.
When the apricot butter is nearly done, prepare a water bath canner, sterilize your jars, and warm your lids and rings.
Ladle the hot butter into jars, leaving ¼ inch headspace. Wipe rims, apply lids and rings, and process in a boiling water bath for 10 minutes (for both half-pints and pints). Adjust processing time for altitude as needed.