What is RRCConnectionReestablishmentRequest in LTE?

It is the uplink LTE RRC message the UE sends to request recovery of a broken connected RRC context.

What usually comes after RRCConnectionReestablishmentRequest?

The network usually responds with RRCConnectionReestablishment or RRCConnectionReestablishmentReject.

What should I inspect first in RRCConnectionReestablishmentRequest?

Start with reestablishmentCause, the UE identity fields, and the next recovery outcome.

How is it different from RRCConnectionRequest?

RRCConnectionRequest starts a fresh connection. RRCConnectionReestablishmentRequest tries to recover an earlier broken connected context.