Do you have a PS4 origional or pro and are you using it via wi-fi or ethernet?

The origional PS4 suffer from horrible wi-fi speed. I had to help a friend of mine with his and even though he has 100 mbit download speeds, the wifi (with an excellent netgear router in the next room at 90% signal strength) would only get him 15 megabits. Wired he got around 60. Although not the full 100 that the other devices get, it was enough to eliminate lag by having him install the router closer and hard wire his PS4 via ethernet. The PS4 Pro, from what I hear, has better wi-fi capabilities, although I've never played with one first hand.

This could be another issue but this would be my first point in helping you troubleshoot.

Thanks for playing FFXIV! I will try to help you in any way I can.