One thing I have noticed about LAN staff in most of South America and even in the US (contracted staff), is there lack of empowerment by the airline itself. Granted this is prevalent throughout South America and especially in Peru.
But the LAN ground agents have little power to "bend" any rules due to IROPS, and even if they do have some leeway are scared to use it for fear for their jobs.
Even the AA staff in LIM has has much more power to take steps if the events warrant them. As has been pointed out in this forum, LAN will book any misconnects into Y (for fear of accidentally booking someone into J) if they rebook you at all.
A number of times I have had AA flights cancelled at the gate and had the GA endorse my ticket over to LAN on the spot (and yes, they still are employed by AA)!