Q:

Ubuntu 16.04 external monitor lags and won't rotate

I just installed a fresh Ubuntu 16.04 on my Lenovo P50, Nvidia M2000M graphics card. When I connect my Dell Ultrasharp U2713HM to the DisplayPort on my Lenovo Dock, and it displays the image fine in the correct resolution (2560 x 1440). 
But there're some serious problems:
(1) It shows an obvious lag or lower framerate, perhaps like 20Hz, when I move the cursor around. This is independent of resolution (also goes for HD and 1024 x 768). When I run xrandr the relevant lines read:
DP-1 connected primary 2560x1440+0+0 597mm x 336mm
    2560x1440     59.95*+

(2) Perhaps connected to (1), the cursor leaves some "pixels" behind as if the graphics card "forgets" to update the image. These disappear when I try to take a screenshot or whenever that part of the display changes in any way.
(3) There's no option for rotating the display. The Display GUI dialogue only has "normal". I usually work in portrait mode (rotated counterclockwise) so this is annoying. Using xrandr fails as well:
$ xrandr --output "DP-1" --rotate left
xrandr: output DP-1 cannot use rotation "left" reflection "none"

What I tried:

Changing between nouveau and Nvidia drivers, rebooting after each change. No difference in lag, mouse trail, or rotation. So this is not obviously a driver problem.
Installing the newer nividia-364 driver from a ppa. It broke the login screen, which just kept playing the drumroll over and over. I had to boot into console (failsafeX failed...) and uninstall.

Some relevant observations:

In the Ubuntu Display dialogue, pressing the monitor illustrations caused a significant lag, perhaps 20 seconds before the dialogue became responsive again during which the fan began rushing, indicating heavy processing.
Relevant lines from lspci:

.
01:00.0 VGA compatible controller: NVIDIA Corporation GM107GLM [Quadro M2000M] (rev a2)
00:02.0 VGA compatible controller: Intel Corporation Skylake Integrated Graphics (rev 06)

A:

Following this guide solved the problem. I did all of it: updated GRUB settings, BIOS settings, and the kernel. I haven't tested whether all of these are necessary but at least the full package did the trick for me.
It works on the P50's mini-DisplayPort. However, when my external monitor is connected to either of the Lenovo Dock's Displayports, it simply doesn't detect the external monitor in the Ubuntu's Displays dialogue or xrandr.
I'm using nvidia-361.

