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   ...