In a saucepan, combine the chopped fresh figs, sugar and water over medium heat. Stir to dissolve the sugar.
Add the fresh rosemary sprig to the mixture. This will infuse the jam with the aromatic rosemary flavour. You can tie the rosemary sprig with kitchen twine for easy removal later.
Bring the mixture to a simmer and cook for about 10-15 minutes, stirring occasionally. The figs should become soft, and the mixture will thicken to a jam-like consistency.
Remove the rosemary sprig from the jam and discard it. Stir in the lemon juice to brighten the flavors. Let it boil for another 5 minutes. Allow the fig jam to cool.