I connect my television to the computer via HDMI, while my desktop monitor is attached via a DVI cable.  This allows me to have them both operational at the same time.  I'm sure many other people have a similar arrangement.

My previous (generic-branded) television gave up the ghost recently, so I had to buy a new one.  KDE had no problems with the former, whereas the latter (Toshiba 40L3650) unfortunately wreaks havoc while logging in and with the lock screen.
* https://toshibatv-ap.com/sg/en/models/40l3650/

Specifically, the KDE-launching process takes much longer than usual.  I occasionally get a dialog box to say that 'ksmserver' has failed altogether.  KDE then works normally, until I (eventually) get to the lock screen.

The problem there is that the password field is unable to receive the focus.  Clicking on it, or trying to tab my way to it, has no effect.  This means I can't enter my password to unlock the system!

My only option then is to switch to another terminal and kill the lock screen manually.  To get around the problem, I've been using good old 'xlock'.  It's far from sexy (by modern standards) but will do for the moment.

If I turn the TV off or unplug the cable, both problems go away.  I know it's not X11-related, as LXDE logs in instantly with both screens active.  Furthermore, there's nothing unusual going on in the X11 log files.

FYI, it doesn't matter what 'kscreen' settings I use.  Whether the outputs are unified or not makes no difference to 'ksmserver'.  Should I be setting some specific monitor settings for the new TV in my X11 configuration file?