If you are having such a big performance issues, you should check your PC in general, unless if you are using a 15 years old rig.
I use for testing purposes a 2012 FX CPU and i never experience such a lag, the game is playable normally, just having performance drops in intense fights, but lagging from the start to the end of the game, no, thats not normal and you should check it out.
But its better to clear a few things out about new version:
The performance is much better there, but if anyone believes that the game cannot lag, thats not possible due to game engine limitations and network protocol design.
None can fix these except Blizzard, so there will always be someone having a "weak PC" or a "Weak connection" which will lag the game and all the players being in that game.
There's a difference between "PC lag and Network lag", (worst is PC lag), but the results are kinda similar.