Since the game moved to Steam we are without a native linux client. After a few unsuccessful attempts to get the game running smoothly on Linux in 2014 I resorted to rebooting to windows to play for the time being.

New attempt eight years later tldr: This is smooth... (and way too much fiddling for any sane person)

My Setup:
E5-2680v3
64GB RAM
Radeon 5700XT
Behringer UMC204HD
2x 1440p display

ArchLinux
X11 based window manager
pulseaudio
native linux steam client + lutris

Installed Quakelive via Lutris and it starts up just fine, runs at decent FPS but microstutters every now and then.

Big issue: Noticeable delay on the sound. While there is a switch in Lutris System Options called "Reduce PulseAudio Latency" it had no reasonable effect.
Solution: set the environment variable

PULSE_LATENCY_MSEC=10

in the Lutris quakelive system options. You can try to go even lower, but on this system the sound got distorted at values below 10ms.

How to get rid of microstutters?
Quakelive has no multithreading, the process just runs on a single CPU core and tends to max it out. Every modern processor will move such a workload between its cores to heat the die evenly. Whenever the process gets moved to a different CPU core, you might get a tiny stuttering effect.
Solution: pin quakelive process to a single CPU core by running

taskset -pc 10 $(pgrep quakelive_steam)

after the game is started. This pins the quakelive process to logical CPU Core 10. However - the Kernel will still schedule other processes on this CPU and depending on your background processes, it might interfere with our quakelive process from which we assume that it runs best, if it has its own dedicated core of which it can just use the full 100%. Luckily there is an option to remove CPU cores from the normal Kernel CPU scheduling. Adding

isolcpus=10 nohz_full=10 rcu_nocbs=10

to the Kernel command line in the grub config frees our CPU core 10 from any "random" scheduling and we have a dedicated core just for our quakelive process, which we can schedule with taskset to core 10.

This had noteable effect, but there were still instances of microstuttering noticeable here and there.
Ugly solution: It looked as if microstuttering was corelated to what was happening on the second monitor (discord message, audio player changing cover art and whatnot). Disabling the second monitor was the only approach to get rid of that so far.

Result: A Quakelive experience at least as smooth as on Windows.

Was it worth putting in the effort? Since I enjoy torturing myself with the Linux on Desktop and gaming on Linux game, 100% yes. Not having to reboot leads me to playing the game more often.