Prepare the apples: Wash the apples, remove damaged areas, and cut them into small pieces. Leave the skins and cores on to retain natural pectin.
Cook the apples: Add the apples and water to a large saucepan. Bring to a boil, then reduce the heat and simmer until the apples are very soft.
Strain the juice: Transfer the cooked apples to a damp jelly bag or cheesecloth and let the juice drain naturally. Do not squeeze the pulp if you want clear jelly.
Measure the juice: Measure the strained apple juice before adding sugar. Use about ¾ cup sugar for each 1 cup of apple juice.
Combine: Add the measured apple juice, sugar, and lemon juice to a clean large pot.
Bring to a boil: Heat over medium-high to high heat, stirring until the sugar dissolves and the mixture reaches a full boil.
Cook the jelly: Continue cooking until the mixture reaches the proper jelly stage. At sea level, about 220°F is the usual endpoint for jelly without added pectin.
Remove foam: Take the pot from the heat and skim away any foam from the surface.
Fill the jars: Ladle the hot apple jelly into prepared jars, leaving the recommended headspace for canning.
Process and cool: For shelf-stable storage, process the filled jars using a tested boiling-water-canning method. For refrigerator jelly, cool, cover, and refrigerate.