Now that Skype for Business 2016 for Mac is publicly available, you could get rid of the old Lync for Mac 2011. Preferably, this should be a clean uninstall. Microsoft has released KB2691870, explaining how to do this.

The uninstall is not very elaborate: dragging the Lync application to the Trash is sufficient but leaves configuration, preferences and chat history on your Mac. To get rid of those, remove the following files:

• ~/Library/Preferences/com.microsoft.Lync.plist
• ~/Library/Preferences/ByHost/MicrosoftLyncRegistrationDB.*.plist
• ~/Library/Logs/Microsoft-Lync*.log

Remove these folders:

• ~/Documents/Microsoft User Data/Microsoft Lync Data
• ~/Documents/Microsoft User Data/Microsoft Lync History

All that's left are things left in Keychain. Open the Keychain Access application, and look for any keychains resembling OC__KeyContainer__<email address>, and delete them. If it's an on-premise Lync server you were connecting to, there will also be a <your email address> certificate in the Login keychain, which can be removed as well. Finally, remove any files from the keychain folder (~/Library/Keychains) resembling OC__KeyContainer__<email address>.