Yep, this is 'iffy' at best. These instructions did not work for me either. I tried several things, and honestly can't remember what I did to finally get it working on an iPhone. I did log out of the Lastpass app but it still took several tries before and option to "use <email address> account" showed up as a choice.
I'm now trying on an android device for another account and it refuses to do a cloud backup even though all the steps seem to have finished properly. I uninstalled and reinstalled Lastpass Authenticator with no effect. I just get the "your authenticator accounts couldn't be saved to the cloud" error message repeatedly and it never enables. I've tried so many combinations of Lastpass app logged in/logged out, biometrics enabled/disabled, enabling/disabling the authenticator from the vault, and other tweaks to settings. Not sure what the magic combination is, but I've worked on this for a couple of hours now and can't get backups working.
