Remove stems from fresh figs and halve them as directed in the ingredient list. Place the prepared figs in a large heavy-bottomed pot or Dutch oven, then add the sugar and salt. Stir well to coat the figs evenly—this helps draw out their natural juices and begins the preserve-making process. Let this mixture sit undisturbed for 30 minutes, which allows the sugar to dissolve slightly and the figs to release their liquid.
After the 30-minute rest, add the water and lemon juice to the fig mixture. Place the pot over medium heat and stir frequently until the sugar has completely dissolved and the mixture begins to bubble gently. Once the sugar is fully melted, reduce the heat to low and add the lemon rind strips. I like to keep the rind in a few larger pieces rather than too finely cut—this makes them easier to remove later and gives a more elegant appearance in the finished preserve. Simmer gently for 45 to 60 minutes, stirring occasionally to prevent sticking on the bottom.
The preserve is ready when it has thickened noticeably and a spoonful dropped onto a cold plate wrinkles slightly when pushed (around 220°F on a candy thermometer, though testing by feel works well). Remove the pot from heat and carefully fish out the lemon rind pieces with a slotted spoon or fork—discard them or set aside if you prefer a bit of rind for texture. Stir in the vanilla extract for a subtle flavor note. If there are any large fig pieces remaining, gently mash them with the back of a spoon to create a more uniform consistency. Pour the hot preserve into sterilized jars, leaving about 1/4 inch of headspace, then allow to cool completely at room temperature before sealing.