While I was helping out a co-worker; we could not get Lync to properly work on the desktop. So during the course of troubleshooting; we reset the password for the Office365 account.
After the password reset, with a different symbol, the Lync client was now happy.
While looking at the original password; it had a \ in the password.
It appears you can change your password in Office365 with a \ symbol. But the Lync client will not log in with a \ symbol in the password string.
Summary: It appears you cannot have the \ symbol in your password if you plan on using Lync with Office365.