I have been having issues with lag on the ps4 as well. Regularly get "Lobby Service Connection had an error." There are many times in dungeons when the game lags by about 20 secs and it catches up as everything is dead.
Again this is happening on the PS4. It was fine a month ago too. The connection was wireless and wired with the same result. And it seems to be happening in instances 90% of the time and 50% in world.
So far I have reset the router, (game runs fine on roommates PC). And cleared the cookies on the PSN browser and made sure the accept cookies was still on the PSN browser and resetted the PS4.
Any other steps would be appreciated.