Start by placing the figs in a bowl and covering them with boiling water for 10 minutes. This will soften the skins and flesh.
Place the water, thyme, and lime zest in a heavy-bottomed pan. (Make sure you count the number of zest strips so that you know how many to remove.)
Stem and coarsely chop softened figs, and add to the pan.
Add the sugar and stir well.
Bring to a boil over medium heat, stirring occasionally.
Once boiling, increase heat to medium-high and boil until thick, stirring often to prevent scorching. This will take about 10 minutes.
Take off the heat and remove the thyme bouquet and lime zest strips with tongs.
Using an immersion blender, purée the figs until “chunky-smooth.” (You will need to decide what that means for you - do you like it chunkier or smoother? There is no right or wrong!)
Add the lime juice and boil for one minute longer, stirring constantly.
Scrape the jam into decorative pots, bowls, or jars.
Let cool to room temperature.
Cover with plastic wrap or jar lids, and keep refrigerated.