Nowadays it is technically possible to add Skype contacts to Skype for Business, but external communication needs to be allowed from Skype for Business admin center (Office 365), first.
Let Skype for Business users add Skype contacts
Sign in with your Office 365 admin account at https://portal.office.com/adminportal/home.
In the Office 365 admin center, go to Admin Centers > Skype for Business.
In the Skype for Business admin center, choose organization > external communications.
- Choose Let people use Skype for Business to communicate with Skype users outside your organization.
- WAIT UP TO 24 HOURS TO TEST
This is a shortened version. The original documentation linked goes through all the settings.
All these settings are company-wide i.e. affecting the whole Office 365 tenant.
If you have Skype for Business Server 2015, you'd need to Deploy Skype Connectivity.
Skype for Business Server 2015 uses the federation access architecture
to support connectivity with Skype. This connectivity enables your
Skype for Business Server users to add Skype. Skype clients can also
add Skype for Business users to their contact list. Based on policies
administratively set in Skype for Business Server users will be able
to communicate using instant messaging, see each other’s presence, and
initiate audio and video calls.