Livepatches are only produced for supported kernels, and only for CVEs that require a Linux kernel modification to fix the problem (for example, a CPU bug may not have a kernel fix). Further, livepatches do not address security problems in Ubuntu software packages, or in third-party drivers that do not ship as part of the Linux kernel (i.e. NVIDIA GPU drivers).
Livepatch is intended to provide protection from security issues in addition to regular kernel security updates, so be sure to read and follow the security advisories published in Ubuntu Security Notifications (USNs) for your kernel.