Hi Hyon,
I have looked through the whole thread, and I would like to remind that to connect Lync for Mac 2011 to Lync Online in Office 365, we need to have Lync for Mac version 14.0.6 or a later version installed. If you use a version that's earlier than version 14.0.6, you may have problems when you sign in to Lync Online because earlier versions have issues that prevent authentication to Lync Online. Please find the latest update at the following Microsoft website: Update for Lync for Mac 2011
In addition, to narrow down the cause, would you mind performing some steps to see if the issue persists? Please see the following:
1. Try to sign in to Lync by using an incorrect sign-in address which you know won’t work. For example, \EmailAddress @contoso.com. After the sign-in fails, please use the correct sign-in address.
2. Clear cached data.
First, delete the following folders:
Users/Home Folder/Library/Caches/com.microsoft.Lync
Users/Home Folder/Documents/Microsoft User Data/Microsoft Lync History
3. If the certificates for Lync is corrupted, please delete it. To do this, follow these steps:
a. Open the Keychain Access certificate management utility. To do this, in Finder, click Applications, click Utilities, and then click Keychain Access. Or, search for Keychain Access by using Spotlight.
b. In the left pane, click login, and then click Certificates.
c. In the right pane, find a certificate that's named Unknown or Communications Server, select it, and then delete it.
Note You may have to unlock your keychain by using your password.
d. Close Keychain Access.
e. Restart Lync for Mac.
Thanks,
April Zhou