The Lync client logs are surprisingly useful in troubleshooting. In 2010 and 2013 the log paths are different, here are the shortcuts to the locations regardless of the drive the user profile is on
Start, Run, and Paste:
Lync 2013:
%LOCALAPPDATA%\Microsoft\Office\15.0\Lync\Tracing\
Lync 2010:
%UserProfile%\Tracing
Typically, if user profiles are on the C:\ drive these take you to
C:\Users\UserName\AppData\Local\Microsoft\Office\15.0\Lync\Tracing
C:\Users\UserName\Tracing