For LTE emergency call if authentication gets failed still network serves the UE based on IMEI. If UE does not have IMSI, IMEI will be used to identify the UE and if IMSI is there but it is unauthenticated network stores unauthenticated IMSI and provide emergency services to UE.
LTE emergency call flow is as same as LTE normal attach w.r.t to messages exchange point of view, here is the call flow -
Reference:
http://wired-n-wireless.blogspot.in/2012/04/ims-emergency-calls-over-lte-short.html