For the caramelized figs: Melt coconut oil over medium heat in a saucepan. Add coconut sugar and water, stir to dissolve. Halve all of the figs and toss in the saucepan with lemon juice. Cook over medium heat, stirring frequently, until you have a fairly chunky, jam-like mixture. This should take about 25-30 minutes, or so. Add salt, give it a stir, set aside and let cool completely.
Ice cream: Put the coconut milk and dates in a blender and puree until smooth. Add the almond milk (or other non-dairy milk), vanilla extract and thickener (if using). Puree until smooth. Refrigerate for about an hour or so, until cold.
Using an ice cream machine, pour the ice cream base into the frozen basin and process according to manufacturer instructions, i.e., let spin and thicken for 20 minutes. Then add in the fig jam mixture and the toasted pistachios. Continue to process for around 10 minutes. Pour the semi-frozen mixture into a pyrex dish or glass tupperware. Freeze for at least two hours before serving.