The bookworm PPA software doesn't (currently) have a release compatible with the version of Linux Lite being used which is jammy based.
This conflict is causing the update process to error.
The bookworm PPA software should be removed from the system and then the PPA needs to be removed from the update list.
Removing the PPA from the update list should allow the update to run.
See
https://www.linuxliteos.com/manual/software.html#pparemIf using PPA software, it is important that the PPA has a release that is compatible with the OS in use.
See this link for advice on selecting and installing PPAs
https://www.linuxliteos.com/manual/software.html#ppaAny questions please ask.