I also have the same exact issue (with Ubuntu 20.04.1). Livepatch is running:
> sudo canonical-livepatch status
last check: 1 minute ago
kernel: 5.4.0-56.62-generic
server check-in: succeeded
patch state: ✓ no livepatches needed for this kernel yet
but the 'Software & Updates' Livepatch tab also reports "Livepatch requires an internet connection"... although my machine is online all the time.
I also have the same exact issue (with Ubuntu 20.04.1). Livepatch is running:
> sudo canonical-livepatch status
last check: 1 minute ago
kernel: 5.4.0-56.62-generic
server check-in: succeeded
patch state: ✓ no livepatches needed for this kernel yet
but the 'Software & Updates' Livepatch tab also reports "Livepatch requires an internet connection"... although my machine is online all the time.