In a large, nonreactive saucepan, toss the fig pieces with the sugar and let stand, stirring occasionally, for about 15 minutes, until the sugar is mostly dissolved and the figs are juicy.
Add the lemon juice and water and bring to a boil, stirring until the sugar is completely dissolved. Simmer the fig jam over moderate heat, stirring occasionally, until the fruit is soft and the liquid runs off the side of a spoon in thick, heavy drops, about 20 minutes.
Spoon the jam into three 1/2-pint jars, leaving 1/4 inch of space at the top. Close the jars and let cool to room temperature. Store the jam in the refrigerator for up to 3 months.
Variation: Substitute 1/2 cup of white port for the water and add one 4-inch sprig of rosemary with the lemon juice; discard the rosemary before jarring.