So the following isn't the fault of PermissionsEx, but it is related.

A plugin is accumulating lots of "fake players" and Server.broadcastMessage() is iterating over them all, and I'm hoping there's a way I can use PEX to investigate the issue because it seems that PEX is in control of what's being iterated over (PEX looks like it overrides PermissibleBase.recalculatePermissions() in its Permissibles and has its own PermissionSubscriptionMap). I am unable to report the issue to the plugin author because I don't know which plugin it's coming from.

I also have an unanswered post on spigotmc.org
https://www.spigotmc.org/threads/lag-when-doing-server-broadcastmessage-how-can-i-tell-whats-causing-it.242634/

For details (and maybe more clarity on how it relates to PEX), you can read this thread here:
http://forum.enginehub.org/threads/lag-from-broadcast.16958/

What I'm looking for
Just a way to investigate the issue

Since this seems to be a programming-based question, I'll have to let @zml2008 answer since I don't handle any PEX programming.

In the meanwhile, here's a post over here on the Spigot site about how to do a timings report that may help you figure out what's causing the lag.

You can also look into something called "Warm Roast", which may be able to help you figure out what is going on. (I don't know how to use this application at all.)

Since Citizens is causing the lag, you may want to try their Discussion page to see if anyone knows how to reduce it. Personally, I don't really know how to read a timings report and never used Citizens extensively— I had 2 statues and a couple handfuls of other characters on my server.

Yes, the timing reports helped me narrow it down. I did some learning on how timing reports work (super helpful, glad I learned) but the lag spikes are def coming from citizens, so i will continue to work with them unless the situation changes.

thanks!

You're welcome. Good luck and have fun!