I'm running 10.15.1 Catalina and LogMeIn version 4.1.7284. I have no issues controlling remote clients. I have full functionality. You might try and clear your PRAM and see if that resolves your issue.
There are permissions that need to be set when the client or the host machine is a mac Catalina or a mac Mojave. The first thing is thing is to go to system preferences then security and privacy then accessibilty, Click the lcon to make changes.
Put a check mark in LMI Gui and AEServer and Bash if you see that.
Next go down to full disk access and put a check mark in the same. LMI Gui or Bash pr both
Then screen recorder , check that off as well,
then input monitor
All files and folders and Full DIsk Access
You will see the LogMein Control panel icon in this folders, PLease check mark them and then click the lcok to make changes.
Save then try again.
This information is from a LogMeIN Support Staff.
I've found that adding or ticking the check for LogMeIn in Accessibility and most importantly, in Screen Recording (after Catalina) worked. You don't mention LogMeIn.app. I have that in my list and that is checked on.
I have AEServer in my Accessibility and that is NOT checked on. What exactly does that do?
Being that there are several items in System Preferences that need to be checked, maybe it's best that we get a definitve list. And better would be that LogMeIn does all the check boxes or walks us through all of them like it does for SOME of the settings.
Here are all the possible ones I can find:
Full Disk Access
LogMeIn Control Panel
Files and Folders
I'm working fine with the way mine are set now, but not all of them are checked on so it would be nice to know what all of them do and which are needed on, since I don't have AEServer on and I'm working fine for what I need to do.