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   ...

There's no direct installer available for Skype for Business, as it is part of Office Pro Plus, but if you have enough with the basic version (i.e. you're missing a couple of enterprise grade features), you can get Skype for Business by first installing Lync Basic, then install the required updates to turn Lync into Skype for Business.

1. Microsoft Lync Basic 2013
2. Install these two patches:
   • April 14, 2015 update for Lync 2013 (Skype for Business) (KB2889923)
   • April 14, 2015 update for Lync 2013 (Skype for Business) (KB2889853)