This feature is available for Exchange 2013 / 2016 accounts. 

In order to be able to add regular Skype users as your Skype For Business contacts, you need to submit Skype For Business Federation request.

Once the request is completed you will be able to add regular Skype users to Skype For Business contacts list:

1. Open Skype For Business application and switch to Contacts view. Click a button with the picture of a person and a plus sign > Add a Contact Not in My Organization > Skype.

add_contact

2. Enter Skype username of a person you want to add in the search field.

skype_username

3. Find a user you would like to add as a contact in the list of search results > right-click on a username > Add to Contacts List > select a group you would like to add a user to. 

add_to_list

4. You will see the notification that a contact request was sent.

sent_request

After closing this window you will see the user you have just added in your Skype For Business Contacts list. Note that the user will have pending status in your contacts list and you will not be able to communicate with him until he accepts the request. 

pending_status

Note: If you are not getting notifications when emails are sent from those regular Skype users while everything was set up correctly, check whether external notifications alerts are being blocked. To do so, click on the gear icon located at the top right-hand corner and go to Tools > Options > Alerts and select the Allow anyone to contact me option if it is not ticked.

Alerts