LAN LANPASS - How to get ITA fare for AEP-IGR

I'm trying to book the following, as per ITA for AEP-IGR round trip, july 23-25

Buenos Aires (AEP) to Iguazu (IGR) - Mon, Jul 23
LAN Airlines LAN Airlines 4026 Dep: 1:10PM Arr: 2:55PM 1h 45m Airbus A320 Economy (N)

OPERATED BY LANARGENTINA

Iguazu (IGR) to Buenos Aires (AEP) - Wed, Jul 25
LAN Airlines LAN Airlines 4027 Dep: 3:35PM Arr: 5:30PM 1h 55m Airbus A320 Economy (N)

OPERATED BY LANARGENTINA

Fare 1: Carrier LA NEESP041 BUE to IGR (rules)
Passenger type ADT, round trip fare, booking code N
Covers AEP-IGR (Economy)
$113.81
Fare 2: Carrier LA NEESP041 IGR to BUE (rules)
Passenger type ADT, round trip fare, booking code N
Covers IGR-AEP (Economy)
$113.81
Argentina Domestic Value Added Tax (DL) 111.60
Argentina Gross Receipts Tax (QN) 35.90
Argentina Security Tax (TQ) 2.00
Argentina Airport Tax (XR) 40.36

Subtotal per passenger $269.70
Number of passengers x1

Total airfare & taxes $269.70
Fare construction (can be useful to travel agents)
BUE LA IGR 513.50NEESP041 LA BUE 513.50NEESP041 ARS 1027.00 END XT 111.60DL 35.90QN 2.00TQ 40.36XR

When I look at the LAN website, or call, the cheapest is $468 per person in booking class M. They told me on the phone they have nothing else to offer me.

Who can I call/where can I go to successfully book at the rate identified on ITA?

I get this quite often, see a fare in ITA, cannot book it on LAN, find it on Orbitz, it disappears when I try to book it, find it on AA.com which tells me it is no longer available after putting in my credit card details.

Wait a day or two and LAN will catch up with everyone else's systems (for want of a better phrase) It is almost as if LAN puts its inventory somewhere which is visible to all apart from on LAN's site, but is not bookable. Then a day or two later you can book it.

I'm going a month later and that fare sounds like what I paid.
$230-ish for a 1-way IGR-AEP on LAN with an M fare.

That's what I was seeing trying to book similar flights for earlier in the month on AR. Turned out that you could only get the lower rate as a local resident fare. The ~$450 rate that came up everywhere else was the only rate I could actually book without taking a risk booking a local fare and getting caught without having an Argentinian ID. I'm assuming it's the same for LAN