It does work, I have been using it for a long time now in context of my interest of using a phone as a PC.
https://xdaforums.com/t/phone-as-a-pc.4633441/

Thing is that with just termux, you get just the android/termux environment.
There is a way to get more familiar Linux environments running on your phone by using proot from within termux.
https://wiki.termux.com/wiki/PRoot
For example, using that you can install ARM version of Manjaro, which is basically the same thing that you would run on Raspberry Pi.
But everything in there runs a bit slower, because Proot is some layer that takes up a bit of performance.
Benefit of that is that you can run some Linux software that is not found within Termux packages, but is available in the repositories of other distros. Libreoffice is one such example.

LineageOS 22.2 (on FP4) does not seem to have that option yet.
At least, it is not listed in the developer options.
You can find it if you tap on the search button within developer options (or just general settings, as that also includes results from developer options) and type “terminal” or “linux”.
The (Experimental) Run Linux terminal on Android result shows up.
But after you tap on that, you see that toggle is greyed out. Can’t be enabled.

I am interested in getting that to work, so any help is appreciated.
There is hopefully some ADB command or something that forcefully enables Linux environment.

StackOverflow says that it can be done by editing xrdp.ini:
https://askubuntu.com/questions/133343/how-do-i-set-up-xrdp-session-that-reuses-an-existing-session#360835

Is there a specific reason for choosing RDP?
VNC is the most common protocol in Linux. And RustDesk is also a good, more advanced alternative.

While others already pointed out the similarity to persistent LiveUSB, I would argue that this also feels a bit like Android desktop modes, like Samsung Dex.