Quoting https://assets.ubuntu.com/v1/ac3aa269-DS_Canonical_Livepatch_Service_screen-AW_08.17.pdf :
The Canonical Livepatch Service lets you apply critical
kernel security fixes to your Ubuntu 16.04 LTS and 14.04 LTS
systems without rebooting.
Canonical’s Livepatches are available for the generic flavour
of the 64-bit Intel/AMD (aka, x86_64, amd64) builds of the
Ubuntu 16.04 LTS (Xenial) kernel, which is a Linux 4.4 kernel,
as well as Ubuntu 14.04 LTS running the Linux 4.4 Hardware
Canonical Livepatches work on Ubuntu 16.04 LTS and
14.04 LTS Servers and Desktops, on physical machines, virtual
machines, and in the cloud. Ubuntu 14.04 LTS systems must
use the Hardware Enablement kernel.
So to sum up, at least at this document's time of writing, Livepatch was only available for the 4.4 kernel series of the currently supported Ubuntu LTS releases.
Today 18.04 LTS with the 4.15 kernel is supported too, according to https://wiki.ubuntu.com/Kernel/Livepatch
Anyway, to come back to your actual question, I strongly believe that Livepatch is not compatible with any foreign non-Ubuntu kernel builds. As Arch has nothing to do with Canonical and Ubuntu, it should not be supported.
However (even though it's off-topic for this site), Arch seemingly supports other kernel live patching tools like