This may be a duplicate of Livepatch - Does This Even Do Anything? I have livepatch supposedly running on two machines, one with 18.04.5 LTS 4.15.0-147-generic and one with 20.04.2 LTS 5.8.0-55-generic. I installed it a while ago using the free for personal use system. As I recall at one time it was able to install patches. However, it now always says that I am up to date without ever installing anything. E.g.,
# canonical-livepatch status
last check: 3 seconds ago
kernel: 5.8.0-55.62~20.04.1-generic
server check-in: succeeded
patch state: no livepatches needed for this kernel yet
But it is not true that no patches are needed. There was just a security announcement saying that there was a patch for CVE-2021-3609 applying to this release.