I asked something similar a while ago, which was redirected to this question.
But to elaborate, no you don't have to configure anything differently, because unattended-upgrades and livepatch works in different ways.
- unattended-upgrades runs once per day, and by default includes security updates, including kernel updates which can't be livepatched.
- livepatch runs periodically (multiple times per day), and only patches critical and high-risk kernel vulnerabilities.
It's actually quite few kernel vulnerabilites that are livepatched - in a 6-month timespan, I think there has only been 2 or 3 livepatches for 20.04 (kernel 5.4.0-xx).
So livepatches are actually rare occurences, where regular kernel updates are much more common - which still requires a reboot.
Hope that helps.