If you are upgraded your server to Windows 2012 Server, you might get a "Local Security Authority" error while connecting remotely (through RDP). It comes specially when you are trying to access the server of a different domain with another domain's ID in AD Trust environment. For example if abc.com is in trust with xyz.com and you are trying to access any server in xyz.com with abc.com's account, you may get this error.
The solution is quite simple.
- Login to the server with either local admin account or account of the same domain.
- Go to My Computer's property and click on "Remote settings".
- Disable "Allow connections only from computers running Remote Desktop with Network Level Authentication (recommended)" option by un-checking it.