There are a lot of old search results for enabling “Appear Offline” in Lync or Skype for Business 2016. However, the registry key was missing in my install of Windows 10, so I had to create it to gain access to the feature.
The key should be located here:
HKEY_LOCAL_MACHINE > Software > Policies > Microsoft > Office > 16.0 > Lync
If you don’t see those keys, create them as listed here. Then create a DWORD 32bit and name it EnableAppearOffline. Once created, edit the DWORD and change the value to 1.
Restart Skype for Business and you should now see the “Appear Offline” status option.