The conditions stated on my ticket are different. There is no mention to special conditions for Z fares on US website. I do not deny they are listed on their website in Peru, but in the USA they are not included.
After two months of evasive responses, I end up filing a case with my credit card, so I received my money back.
Lesson learned, NEVER fly again with LAN. Worst customer service I have seen from the airline industry, AND I LIVE IN THE US, where airlines are not famous for great customer services.