Indeed that was the area to investigate. I thought it might be a good idea to create a new user jupyterlab and run everything there (for having all jupyterlab in one place) and I was running systemd in user mode for that user.
And that was indeed the issue, the process got killed some time after I logged off with that user.
The solution was to use loginctl enable-linger (see this systemd issue).
@manics thanks for all your answers and helping me to dissect the issue 