Chop the figs well, add the zest and juice of the lemons, cover with water by about an inch, and simmer over medium-low heat for 2 hours. You want everything to break down and be a mush. Add water as it cooks so it won't stick to the pan.
Get a large kettle of water ready so you can can the fig syrup as soon as it's ready.
Strain the mixture through cheesecloth, then measure out an equal amount of sugar. Return to the pot to reduce to the consistency of maple syrup, or honey -- your choice.
Turn off the heat and push the fig mixture through the fine plate of a food mill. If you don't have a food mill, you could use a drum sieve or a fine colander. But a food mill is best. After everything is through the food mill, pour the fig mixture into a jelly bag if you have one -- I don't, so I used a clean spare undershirt -- and push everything through. You will leave a lot of good stuff in the bag, but it's the price for a clear syrup. If you are OK with a cloudy syrup, just use cheesecloth.
Measure out the fig juice and add an equal amount of sugar. Pour this into a clean pot and bring to a simmer. Let this simmer gently for 10 minutes.
Pour into sterilized pint jars and seal. Process in boiling water for 15 minutes. The syrup should last at least a year. Keep in the fridge once you open it.
This recipe makes about 1 pint and can be scaled up or down.