The ability to communicate with anyone outside your organization is turned off by default in Lync Online (Wave 15 Office 365).
If you want your users to communicate with partners, Skype or any other domain, you have to turn on the options in the portal. Login to the Office 365 portal with your admin account and click on the Lync option in the top left hand corner.
Click on Organization and then External Communications. You can see that the option is set to off by default.
You can switch on external access in two ways – turn it on for only the domains that are explicitly allowed which can be configured further down or turn it on for all expect the domains that are blocked by the admin.
The allowed or blocked domains can be configured further down.
The option to communicate with Skype users and other public IM providers can be enabled by checking the box.
It might take a while for the settings to take effect as it has to be replicated across the Office 365 datacentres.