In my recent experience, getting a refund was a nightmare. I had to call them numerous times and each time I called, the agent told me something different from the previous agent. On top of that, when I supplied the number they had given me, I was repeatedly told that there was no record of my refund request in the system. (And each call center used multiple numbering systems that did not always coincide with one another.) Finally, with a combination of emails and calls to LAN in Miami and Chile, I was able to get the refund. And I speak fluent Spanish!
Make sure you record the date and time of all phone calls, plus the first and last name of the person with whom you speak. Email is easier in this respect because you have everything in writing, however if they ignore your emails you will feel frustrated and powerless.
Forget the online system; just call them and ask them about your status.
I believe they say it takes up to 90 days for the amount to be credited to your account.
Every other airline manages to have a system for refunds that is semi-functional. LAN appears to have shoddy competing systems that undermine one another and ultimately cost the customer.