I had a user having the same errors with LogMein after having issued him a brand new computer and using Migration Assistant to transfer the data (MacOS 10.14.5 to 10.14.5). Since erasing and reinstalling a fresh OS would be too unkind for my people, I logged into another local MacOS account that we create (admin) on the new machine and then had the user launch LogMein from there - sure enough it worked. Since that narrowed the issue down to being user specific, I took a note of all of the User Library files that LogMein had added/modified. They were:
Users/(username)/Library/Preferences/com.logmein.ractrlsafari.xml
Users/(username)/Library/Preferences/com.logmein.ractrlsafari.bak.xml
Users/(username)/Library/Saved application state/com.logmein.ignition.savedstate
Users/(username)/Library/Application Support/Logmein Client
Users/(username)/Library/Application Support/com.apple.sharedfilelist
Users/(username)/Library/Caches/*I forgot to notate the exact file here but it was obviously a LogMein file*
After throwing all of those files/folders in the trash and having the user re-launch LogMein client, everything worked perfectly. It is perhaps the case that only some (or one) of those files (file) needed to be trashed but it won't matter since the LogMein client installer will fill in the gaps.
Anyway, this reached Tier 3 support at LogMein and the best they had was "it must be a Mac thing," so I'm really hoping this helps some people out!