The recent update to Mac OS X Lion (10.7.2) installs an invalid login certificate on most systems, which results in Lync for Mac crashing when it tries to sign in.
Until we get a software update out, there is a workaround that seems to be working for most users that we wanted to let you know about:
1. Open the utility Keychain Access – from Finder to go Applications and then into the Utilities folder. Or just search for it via Spotlight.
2. In Keychain Access – in the left pane click on “login” on the top, and “Certificates” on the bottom.
3. In the right pane, find a certificate with the name “unknown”. Select it and delete it. You may have to unlock your keychain with your password.
4. Close Keychain Access.
5. Restart Microsoft Lync.
This same workaround is also posted on the Microsoft Answers Forum if you would like additional information. Hope that works for you!