The only thing you need to be sure of is that these lower fares are not "Available for residents of Chile only fares".

If you try to book domestic fares on Lan Argentina on the Argentinian version of lan.com, at the final stage of booking it tells you that in accordance with Argentinian law number whatever these fares are only available to residents of Argentina and eligibility will be required to be shown on boarding. It directs non-Argentine residents to the international sites of lan.com.

I don't know whether there are equvalent Chilean fares. If you are able to look at a copy of the complete rules fo the fare in question, there should be a clause titled Sales Restrictions or some thing like that. If it says restricted to residents of Chile then you take a risk purchasing. If it says ticket must be sold in Chile then buying an e-ticket on the Chilean website should be fine.

Unfortunately the fare rules shown on lan.com are not complete.

I think the bottom line is that if going right through the booking process nothing states that there are any of the above mentioned restrictions on sales, then you should be OK.