In case you missed it, there was an important update to the Microsoft Lync for Mac 2011 client last week. Update 14.0.1 addresses issues with signing into Office 365 and with the client closely unexpectedly during sign-in.
I have seen many Office 365 forum postings about the Lync for Mac 2011 client not being able to sign-in, so install this update if you are having any issues.
More information on the issues addressed by this hotfix can be found here: Description of the Microsoft Lync for Mac 2011 14.0.1 update.
The update can be downloaded directly here: Microsoft Lync for Mac 2011 14.0.1 Update.