I have installed Ubuntu 20.04 64 Bit on my Raspberry Pi 4 (with 2 GB RAM). I have also installed lubuntu-desktop.
The system hangs (even the mouse cursor no longer works) after some time (a few minutes (up 30 minutes)) especially when there is some load on the system (like installing packages the require massive compiles (eg python3 -m pip install pandas). But I have also seen the effect without much load (but after a longer time).
I don't see a undervoltage or temperature warning on the screen
not sure it will resolve the problem, but i think i had the same issue, 30 min ago
i found out that 20.04LTS lubuntu-desktop have by default, this option
into settings, click on power, by default, the option automatic suspend is on, yu may set it to off
it fixed my issues, ( after a while my desktop wasnt reacting anymore, only terminal was working on ssh )
since then, everything is fine. hope this help.