Hi @robertallen,
This isn’t something the plugin was made to do out of the box, and therefore outside the scope of support in the forum. With that being said, since it just enqueues the Featherlight script so WordPress can use it, you should be able to make it work with Ajax.
I would follow the instructions in the scripts doc to on using it with Ajax for some ideas: https://github.com/noelboss/featherlight/#usage
Worst case scenario, you can always enqueue the script yourself and initiate it however you’d like.