To chat with a non Skype for Business user, the Skype for Business MUST be the one that adds the Skype user.
To add a non Skype for Business user to your Skype for Business account, you will need to click the Add User button, select “Add a Contact Not in My Organization” then chose “Skype.”
After you chose the “Skype” option you will enter the username you are wanting to add in the Skype Directory tab. Once you do this you will see your contact and you will right click on their username to add them, you will then need to click “Add”.
Once this is complete the user will be added and will be located in your “Other Contacts” group under the Group tab.