web site price differences
 

Data point on web site differences.

BOG-LIM rtn on Peru site $448. US site is $448
BOG-LIM rtn on Colombia site $331.
(All had the Colombia exit tax included)
This is replicated on ITA: using BOG as sales city gives same difference as LIM as sales city. (so tip, do this change when searching ITA)

As well, certain days had different fares differences. i.e. Cheapest fare available on Colombia site on certain day but for the next day on Peru site.

that's the Point Of Sale (POS) hickup. airlines can manage their fare buckets differently for different markets.

although the cheapest fare buckets can still be open for tickets sold in Colombia they might already be closed for other markets. can also be the other way round ...

Fare rules state that the cheaper fare can only be sold in Colombia. LAN often uses weird price discrimination strategies, for instance sometimes the same flights ex-MAD or LHR cost ~300-400 euros less when booked through OTAs (LAN.com doesn't have access to all LAN fares).