Why am I being asked to Restart System even though I have Canonical Livepatch?

I don't know if you managed to find an answer for this, but as I was myself struggling with the same question, I did some research. Security updates are rated from negligible to critical level (there are 5 rating levels). You can check the rating level of each update, running this command:

xargs apt-get changelog < /var/run/reboot-required.pkgs

This will output the whole "history" (changelog) of each package (press "q" to navigate between each listed package) listed in the reboot-required.pkgs file. The most recent update is located at the top of the list. At the right side of each update, you should see an urgency= flag that states its rating. The "critical" rated updates should be automatically applied to the kernel by the Livepatch module, so as to avoid having to reboot the server.

Without the Livepatch module, you would be forced to reboot your server in order to apply the security patch to the kernel.

Lastly, if you want to check if there are services that need to be restarted following the system update, install the needestart package sudo apt-get install needrestart and then run sudo needrestart. This will show you the services that need to be restarted, and give the possibility to restart them right away!

So long story short, you don't need to reboot your server! ;-)