Quite convoluted what you are asking … or try to explain.
The repositories are not stored on the DVD/ISO to install them from there when a new ISO is released. Live media will not store any changes upon reboot, unless you make a persistent USB
But then what? You still have to update via pacman or pamac from the repositories … and seems like you are wanting to do it from live media via chroot on the installed system. Still, repositories are not stored locally, unless you make a local repository