Ubuntu – DisplayPort not being picked up

My mini-PC has Intel i7 running Lubuntu-18.04.
It has 2 monitor outputs, one HDMI and one DisplayPort.
The HDMI port has a HDMI monitor (E2441) plugged into it.
The DisplayPort has a DisplayPort-HDMI converter in it, with a big HDMI TV screen plugged into it, and switched on.

But Menu > Preferences > Monitor Settings (lxrandr) only shows 1 monitor attached.

/var/log/syslog shows:  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011ports:  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011hdmi-output-1: HDMI / DisplayPort 2 (priority 5800, latency offset 0 usec, available: yes)  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011#011properties:  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011#011#011device.icon_name = "video-display"  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011#011#011device.product.name = "E2441"  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011active port: <hdmi-output-1>  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: 2 source(s) available.  

Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011#011properties:  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011hdmi-output-0: HDMI / DisplayPort (priority 5900, latency offset 0 usec, available: no)  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011#011properties:  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011#011#011device.icon_name = "video-display"  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011hdmi-output-1: HDMI / DisplayPort 2 (priority 5800, latency offset 0 usec, available: yes)  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011#011properties:  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011#011#011device.icon_name = "video-display"  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011#011#011device.product.name = "E2441"  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011hdmi-output-2: HDMI / DisplayPort 3 (priority 5700, latency offset 0 usec, available: no)  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011#011properties:  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011#011#011device.icon_name = "video-display"  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011hdmi-output-3: HDMI / DisplayPort 4 (priority 5600, latency offset 0 usec, available: no)  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011#011properties:  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011#011#011device.icon_name = "video-display"  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011hdmi-output-4: HDMI / DisplayPort 5 (priority 5500, latency offset 0 usec, available: no)  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011#011properties:  
Oct 17 07:56:06 i7 pulseaudio[2107]: [pulseaudio] main.c: #011#011#011#011device.icon_name = "video-display"  

The "available: no" seems to be the problem.
Does it need a special driver?

$ xrandr  
Screen 0: minimum 320 x 200, current 1920 x 1080, maximum 8192 x 8192  
DP-1 disconnected primary (normal left inverted right x axis y axis)  
HDMI-1 connected 1920x1080+0+0 (normal left inverted right x axis y axis) 531mm x 299mm  
   1920x1080     60.00*+  50.00    59.94    
   1920x1080i    60.00    50.00    59.94   
   1680x1050     59.88   
   1280x1024     75.02    60.02  
   1280x960      60.00  
   1152x864      75.00  
   1280x720      60.00    50.00    59.94  
   1024x768      75.03    60.00  
   832x624       74.55  
   800x600       75.00    60.32    56.25  
   720x576       50.00  
   720x480       60.00    59.94  
   640x480       75.00    60.00    59.94  
   720x400       70.08  
$ uname -a  
Linux i7 4.15.0-65-generic #74-Ubuntu SMP Tue Sep 17 17:06:04 UTC 2019 x86_64 x86_64 x86_64 GNU/Linux  

This says it will load all HWE modules:
https://wiki.ubuntu.com/Kernel/LTSEnablementStack#Ubuntu_14.04_LTS_-_Trusty_Tahr says for Bionic:
$ sudo apt-get install –install-recommends linux-generic-hwe-18.04 xserver-xorg-hwe-18.04

I tried it, followed by a reboot – but still no change, apart from:

$ uname -a
Linux i7 5.0.0-31-generic #33~18.04.1-Ubuntu SMP Tue Oct 1 10:20:39 UTC 2019 x86_64 x86_64 x86_64 GNU/Linux

External monitor not detected on Ubuntu 18.04 is a similar problem with different hardware.
It seems to show that nobody agrees what fixes it.

What next?

I don't know what any of this means, but maybe somebody does.
$ sudo lshw -c video
name: i915
$ modinfo i915
filename: /lib/modules/5.0.0-32-generic/kernel/drivers/gpu/drm/i915/i915.ko
license: GPL and additional rights
description: Intel Graphics
author: Intel Corporation
…
parm: enable_dp_mst:Enable multi-stream transport (MST) for new DisplayPort sinks. (default: true) (bool)
parm: enable_dpcd_backlight:Enable support for DPCD backlight control (default:false) (bool)
parm: enable_gvt:Enable support for Intel GVT-g graphics virtualization host support(default:false) (bool)
(full listing at https://davekimble.net/problem.DP.txt)

/sys/class/drm/card0/card0-DP-1/status = "disconnected"
/sys/class/drm/card0/card0-HDMI-A-1/status = "connected"