Skylake integrated graphics' DP output
I connected an external LCD via DP to my portable workstation. When under hybrid graphics (Optimus) mode, the external display was not recognized under Trisquel or Debian. However, it was recognized under Ubuntu or Mint (for testing purposes only), though I had to go to Control Center -> Displays and then manually "turn on" the display. Once turned on, the display worked properly. Does this mean that certain (non-free) firmware is required to support dual display on Skylake integrated graphics?
My workaround is to switch to discrete graphics mode (to disable the integrated graphics when I need to use external displays). The discrete graphics card (Nvidia Quadro M2000M, GM107GL-M) seems to work correctly without non-free firmware.
Have You tried running dmesg under Trisquel? When nonfree firmware is prevented from being loaded under linux-libre kernel, a message shoud be generated :)
Hope destroyer: a quick search revealed this: https://www.phoronix.com/scan.php?page=news_item&px=intel-skl-bxt-firmware-blobs
Before I purchased this ThinkPad P50, I knew that Skylake's integrated graphics required firmware, but I wasn't sure whether such firmware was required to support dual display output.
I also purchased a very low-end Skylake mini desktop PC to test VT-d and IOMMU. The mini PC worked smoothly without non-free firmware (only one display). I planned to recommend Skylake to community for security's sake (VT-d was generally supported starting Skylake, both chipset and CPU), but this time I may want to think twice before purchasing another Skylake mini PC. Maybe I can choose those slighter bigger ones with MXM graphics card slot, so I could install a GM107 card (e.g. Quadro M1200-M).
I use my Kaby Lake (sucessor of Kaby Lake) integrated graphics, no discrete graphics whatsoever, and face no problem with external displays. Have you tried a more recent kernel? Install the package "linux-image-generic-hwe-8.0" for version 4.15 or follow the instructions on https://jxself.org/linux-libre/ for more recent versions.
There is another possibility. There are as many as three video output ports on my P50 (one Thunderbolt, one mini DP and one HDMI), and each port has different priority. The port I used was the mini DP (I don't have a Type-C to (mini)DP converter), which had a lower priority, so the display attached to it was considered the 3rd display. Since the integrated graphics support up to 3 displays including the notebook panel, chances are that 2nd display doesn't require firmware but 3rd display does.
I tried both very old kernel (4.15 in Trisquel 8) and very new kernel (5.4 in Debian sid). The display just blinked once before entering the graphical login interface, and it's not recognized in Control Center -> Displays. The display was, however, recognized under Ubuntu or Mint.