played through it once upon release... since "always connected" was very lagging, even for SP... haven't revisited even thou I have the add-on, maybe a re-visit is in order.
Magnum if you have a Nvidia GPU and vsync enabled then the lag you see is the poor implementation of vsync in the game.
I had it too and resolved it by using D3DOverrider (now part of Rivatuner) and pointing it at the Diablo III.exe and using it to force triple buffering and vsync whenever the game is running, and disabled the builtin vsync in the game.
Solved the lag for me.
Frank, I picked up a copy of Diablo 3 for PS4 as well and love how fun it is with the controller much more direct gameplay, I play it a lot using Vita Remote Play.
BTW here is what that Gem of the Hoarder does with one of those trapped chests where you have to survive waves of attackers LOL, $101k loot from fighting off the horde and the 25% chance of gold explosion for each of them, I'm in the money now