I started having these very same issues about three days ago--constant lag (so bad that bosses would still be alive on my screen with plenty of health when they're actually already dead), DC's, 90002 errors... And they occur usually in duties. And the larger the duties, the more lag and disconnects I experience (like Weeping City is practically undoable right now).
I am usually find out in the regular in-game world.
Checked Internet, reset router a few times and tested the connection to my PS4. Speeds are fine. Signal strength is usually 80% or higher. Not 100%, but not low enough to cause this much lag. I recently relocated the PS4, but it has been in its new location (which still isn't that far from the wireless router in my house) for two weeks before these lag/DC issues began happening.
Please, there are so many others having this issues (and others that have had these issues for longer than me), please figure out what is wrong and fix the issue. The game is 50% unplayable for me and so many others right now. :(
Also, like someone else said--connections to the official forums and Lodestone have also been bad. I've gotten several "Connection has timed out" errors while trying to access the Forum.
