Your logs don’t show the login process. It would appear your client is able to find the registrar as you’re getting a prompt for credentials. Presumably this Lync Client is in a different domain though to the Lync Server? As by default Lync will use KerberosSSO presuming you’re internal and in the same domain as the Lync Server.
Is this affecting all users? Or just one user? If using a proxy on the client PC disable and retest. Is the user signing in internally or externally? Can you provide new logs with the complete sign in process. You can use the OCS logging tool on the Front End and get the logs that way or from the client. Either will suffice.