I've noticed that the BA online search engine has stopped recognizing some LAN cities, like Mendoza MDZ and Buenos Aires AEP. However I've still had luck using AA miles last month reserving LAN flights. Qantas's award engine also doesn't have all the cities listed, at least when put in the departure field.
Reading between the lines, I think you'll have problems using online tools to find LAN availability short of calling in to AA. I've tried using LAN's online site, and whatever they are offering at the lowest km redemption rate I've found the best luck when asking AA on it. However, the inventory shown on LAN.com isn't 1:1 bookable on AA, as I think more seats are available to LANpass members.
I'm also still struggling to figure out best way to check availability online. ExpertFlyer doesn't support LAN, either.