It seems that in the latest version of Lync for the iPhone/iPad/iOS Microsoft have tightened up on the certificate checks. I hit this issue with a customer that had a public CA cert on their reverse proxy, but only an internal cert on a dev/test Lync 2013 edge. Previous to 5.4 Lync mobile signed in and worked fine, but on 5.4 it threw a cert error. The simple fix is to install the root cert/chain on the device.
If you are seeing this error, ensure you have the root cert/chain installed on your device (protip, you can email it to the device, even though you can’t open the certificate attachment in Outlook you can on the device).
You shouldn’t really hit this in an environment with proper public certificates from a provider trusted by iOS.
Update 2/5/2013: MSFT have now posted a KB on this: http://support.microsoft.com/kb/2965499/