I've only had this done the one time - and it was done by the agent on the AA RTW desk; I was making a heap of changes to my LONE4, he put in the request to BA (electronically) and continued with my other changes; before he had finished he received the response from BA granting the seats.

Are you flying AKL-SCL or SYD-SCL?
LAN has V class seats AKL-SCL but only the higher M class seats SYD-SCL (M is higher than L)

I would ring the local LAN office and ask them