If you want Hinano (Local Beer) they will have it on the ship or you can get it off the dock. If you want other stuff, there are a few Duty Free Shops at LAX right in the front of the terminal. They deliver your purchase to you at the gate just before you board the plane at ATN.

VOYAGER:
MC to FLL 11/07
MC/Dover 6/06
MARINER:
BCN / Ven 10/11
Alaska 2001|2006
Panama Canal 2003
NAV
Caribbean 11/06
Bermuda|New Eng/Canada 6/04
PG 5/05
OCEANIA
Nautica |Ist/Athens 6/07
Regatta|Baltics 6/08
Riviera 2013 Crossing -Istanbul to Miami