Further to my question.....
Found the knowledge base item:
support.microsoft.com/.../2803796
This issue occurs because Lync for Mac 2011 incorrectly reads the system time. Therefore, the web ticket that Lync for Mac 2011 tries to use is expired. This issue occurs when your current time zone is the Pacific Time zone or a time zone west of the Pacific Time zone. If you change the system time zone to a time zone east of the Pacific Time zone, you can sign in to Lync Online by using Lync for Mac 2011. For example, you change the time zone from the Pacific Time zone to the Eastern Time zone.
This is fixed in the Lync 10.0.4 update described at:
support.microsoft.com/.../2778095
However running the update did not solve it when we originally tried, instead we ended up with two instances of Lync being reported on the mac. However, deleting the two instances and reinstalling with the update before we tried to log in created only one instance, and then the first logon attempt ran ok. For some reason the update failed the first time, but we also got the unusual "unidentified developer" issue so somewhere a code signing or keychain issue probably caused the extra hiccup that isn't covered in the Microsoft Knowledgebase article. Hopefully this response might help others.