Get the canning setup ready by washing and sterilizing 5 to 6 half-pint jars, then keep the jars hot while the lids rest in hot but not boiling water. Having everything warm and ready makes filling easier and helps the jam stay hot from pot to jar.
Rinse and sort the blackberries, discard any stems or debris, and mash them with a potato masher in a large bowl or directly in the jam pot. Plan on about 2 cups whole berries to make 1 cup mashed fruit, and crush well so large chunks do not slow the set.
Put the mashed berries in a large deep jam pot and stir in the sugar and lemon juice until evenly combined. Mixing before heating starts dissolving the sugar and gives the fruit a more even boil.
Set the pot over medium-high heat and bring the mixture to a steady boil, stirring often as it heats. Blackberry jam foams heavily, so stay close once it starts bubbling and scrape the bottom of the pot to prevent scorching.
Boil the jam, stirring constantly, until it thickens and reaches gel stage, usually in 20 to 30 minutes. Watch for the color to turn a glossy deep purple, the aroma to grow warmer and more intense, and the foam to begin subsiding as the jam nears readiness.
Take the pot off the heat and skim off any foam left on the surface if you want a clearer finish. The jam should look shiny and thick rather than loose and frothy.
Ladle the hot jam into the prepared jars, leaving 1/4 inch headspace, then wipe the rims clean and apply the lids and bands to fingertip tight. Clean rims and even headspace help the jars seal properly during processing.
Lower the jars into the boiling water bath so they are covered by 1 to 2 inches of water, then process for 10 minutes, or 15 minutes above 6,000 feet. The water should return to a full boil around the jars while they process.
Lift the jars out and let them cool undisturbed for 12 to 24 hours before checking the seals, labeling, and storing. As they cool, the lids should pull down and the jam will continue to settle into its final texture.