What is System Information Block Type 3 in LTE?

It is the LTE broadcast block that gives the UE serving-frequency cell reselection rules for idle-mode mobility.

Why is LTE SIB3 important?

Because it often explains why an idle UE stayed on the serving cell, reselected, or behaved differently across cells even when access itself looked normal.

What should I inspect first in LTE SIB3?

Start with the serving-frequency and intra-frequency reselection information, then compare those rules with the observed idle radio conditions.

How does SIB3 relate to SIB4 and SIB5?

SIB3 gives the serving-frequency rules. SIB4 adds same-frequency neighbor-cell detail, and SIB5 covers inter-frequency LTE mobility.