Since the days of OCS there has been a method to manually configure Microsoft’s UC clients with a specific server address for internal & external sign-in capabilities.  If the clients were not hard-coded to utilize a certain server FQDN, the UC clients would begin an automatic server discovery process to auto-magically find where it should attempt to register.  If you’re looking for information on how that works, I would suggest starting here:

Office Communicator Sign-In and Discovery

Lync 2010 DNS Requirements for Automatic Client Sign-In

Lync 2013 DNS Requirements for Autodiscover

When you’re in a Hybrid scenario and you want to bypass the on-premises automatic sign-in process (reasons are myriad why you would potentially need to do this – a separate discussion for another time), you can hard-code the server discovery address for both the Lync desktop clients and the Lync mobility clients:

Lync 2010/2013 Desktop

Internal server name:  sipdir.online.lync.com:443
External server name:  sipdir.online.lync.com:443

Lync for Mac

Internal server name:  sipdir.online.lync.com:443
External server name:  sipdir.online.lync.com:443

Skype for Business Desktop

Internal server name:  sipdir.online.lync.com:443
External server name:  sipdir.online.lync.com:443

Lync 2010/2013 Mobile

Internal discovery address:  webdir.online.lync.com/Autodiscover/AutodiscoverService.svc/root
External discovery address:  webdir.online.lync.com/Autodiscover/AutodiscoverService.svc/root

Skype for Business Mobile

Internal discovery address:  webdir.online.lync.com/Autodiscover/AutodiscoverService.svc/root
External discovery address:  webdir.online.lync.com/Autodiscover/AutodiscoverService.svc/root

The “:443” is required for the desktop clients to force registration (and all subsequent communications) to flow over the firewall friendly TCP 443 port.  If you forget, the desktop clients will attempt to utilize TCP 5061, which will result in a sign-in failure.  For the mobility clients, the entire URL string is required.

Again a word of caution here that manually configuring these entries will bypass any automatic client sign-in detection.  If you configure these settings for your Office365-homed account and then migrate back on-premises, your client will fail to sign-in.  Please make sure you understand the ramifications of manually configuring these settings!