Update 2023-03-05: It appears that the canonical-livepatch does not support the 5.19 HWE Kernels at this time. Even a clean install of 22.04 LTS is not supported that comes with the 5.19 Kernel (probably never supported). However, it does appear that support for the HWE 6.2 Kernel is coming in July 2023, see: https://ubuntu.com/blog/canonical-livepatch-gets-even-better-now-supporting-hardware-enablement-kernels And now as the 6.15 Kernels have come out, they are not supported by canonical-livepatch at this time. My guess is that since we are a few months away from 24.04 release that the Kernel version then will be supported in that release.
$ canonical-livepatch status
last check: 40 seconds ago
kernel: 5.19.0-35.36~22.04.1-generic
server check-in: succeeded
patch state: ✗ kernel version not supported
tier: updates (Free usage; This machine beta tests new patches.)
machine id: <redacted>
$ canonical-livepatch status
last check: 55 minutes ago
kernel: 5.15.0-67.74-generic
server check-in: succeeded
patch state: ✓ no livepatches needed for this kernel yet
tier: updates (Free usage; This machine beta tests new patches.)
machine id: <redacted>
*Updated answer for pro instead of ua.
If you have an Ubuntu One account, you can do Livepatch for HWE Kernels for personal use on up to 3 5 systems. You will need to get a token for it to work.
Visit https://auth.livepatch.canonical.com/ to get your token.
Once you have your token you should be able to activate Livepatch on your system using the pro tool.
sudo pro enable livepatch <token>
Then Livepatch should be working for HWE Kernels. (See note above since this was working at the time with ua and not pro)
terrance@terrance-ubuntu:~$ canonical-livepatch status
last check: 45 minutes ago
kernel: 5.13.0-30.33~20.04.1-generic
server check-in: succeeded
patch state: ✓ no livepatches needed for this kernel yet
tier: updates (Free usage; This machine beta tests new patches.)
machine id: <redacted>