At the moment, when using Discover on a live system, you're able to install updates, which shouldn't be allowed. On a live system, discover should still be able to install and uninstall apps, but not perform system updates. So maybe this could just be a configuration option which hides the update option on the left pane. I originally filed this issue downstream here https://pagure.io/fedora-kde/SIG/issue/60
Discover can "discover" (lol) from the kernel command-line whether or not we're running on live OSes by looking at kernel args to see if "rd.live.image" is in the kernel command-line. Discover can self-disable by default when that is present in the kernel command line.
I'm not necessarily convinced this is a good idea. Live users should be able to update/install items if they wish (even if it's not necessarily a good idea)
Discover offers support for "Offline Updates" which implements this feature. Distros get to choose whether it's on or off by default, and a number have opted in--at least Fedora and Neon, off the top of my head. Users can also opt in if their distro doesn't do this.