SOLUTION FOUND!
Just had success with this issue!
Open a Finder window and go to Library > Application Support > LogMeIn.
There you will find a Command Prompt Uninstaller. Don't be afraid of it.
Open in, and when prompted, type in your password (if you don't have one, just hit the return key).
And Bob's your uncle! The folder plus the stupid tray icon will be ejected from your system!
This was the last trace of LogMeIn found on my computer. May it finally rest in peace!
Hope this helps guys!