What is Authentication Failure in LTE?

It is the EPS NAS message the UE sends when it cannot complete the authentication challenge normally.

What should I inspect first in Authentication Failure?

Start with the EMM cause, then check whether the authentication failure parameter is present.

What usually comes after Authentication Failure?

The network may retry authentication with a new challenge, send Authentication Reject, or stop the current procedure.

Why is Authentication Failure important in troubleshooting?

Because it shows the authentication branch failed on the UE side before a normal Authentication Response could continue.