Chat lag is due to the way chat is designed and implemented in this game. Pretty much all channels have a passive “poll for messages” implementation they describe as an asynchronious messaging system akin to mailing in many MMOs where you interact with a postbox or letter box, and then send a message to the intended recipient. However, due to the UI of the messaging system looking far more familiar to that of a standard MMO synchronous messaging system where all messages get pushed out to all connected clients, chat lag is indeed a thing, and its a real, major problem. However, the devs seem to think the performance of this asynchronous chat system is far more beneficial than that of a proper instant-messaging system like IRC where everything is pushed out to clients from the central server.
Just a note, @james @Leahlemoncakes and crew, IRC is infinitely scalable. Replace the current chat system with one powered by IRC, and I’m sure you can infinitely scale a chat system that can PUSH messages instantaneously to clients, eliminating chat lag from the game.
See the release notes here Testing 210: Guilds and Messaging++! where the devs go into more technical detail about the system. An overhaul is necessary here.
An excerpt of the details regarding chat channels and PMs.