External monitor on Lenovo ThinkPad laptop blacks out randomly

Not enough power seems to be the issue, based on two working solutions:

  1. I changed my setup to use a Lenovo docking station. That is, my new setup is 95W PSU → dock → (laptop, two screens connected via DisplayPort, mouse and keyboard).
  2. A colleague (their permalink system is broken, it's the 61st message in that thread) with the same problem simply changed the PSU for the 95W one delivered with the Lenovo docking station and the problem went away. That is, their setup is still PSU → laptop → HDMI → monitor, just with a higher-power PSU.

Since the common factor is the PSU it might be concluded that running off the default 65W PSU is the problem, and using a 95W PSU solves it.

[I'll report back if the problem comes back for either of us, but so far the symptoms have disappeared.]