There's a fairly complete list of miles expiration policies here:
http://thepointsguy.com/2013/04/airl...icies-roundup/
I have the regular LanPass Visa card, and I've been told that I can reset the expiration of my LanPass kms by flying a paid LAN flight. I have not looked into whether that would count paid AA flights with a codeshared LAN flight number or not. But even if not, I can afford to fly a paid LAN flight every two or three years until I no longer have their LanPass kms. If you can't, 3 years doesn't sound very good, compared to Korean Air, which is 7 years if you believe the chart at the link but 10 years if you believe the text further below on that page!
Avianca LifeMiles is not listed there, but here:
https://www.lifemiles.com/eng/abo/wnb/wnbtercond.aspx
it explains that expiration at that airline (unilike the other 3 you asked about) can be reset by
any account activity:
Any activity in the member’s LifeMiles account extends the expiration date of the mileage credit of that account for a term of twenty four (24) months from the date of the latest qualifying activity. Qualifying activity is defined as any mileage accrual or redemption transaction, affecting the member’s mileage credit. Twenty four (24) months after the latest activity all miles will expire and the mileage credit of the account will be zero (0) miles. LifeMiles Corp and/or the Airlines may, but shall not be responsible for establishing special conditions to reactivate expired Miles and may also establish a charge for their reactivation.
This thread on FT suggests a couple easy ways that reset it (though the final verdict on whether donations of less than 100 miles actually work on was never reported):
http://www.flyertalk.com/forum/avian...lifemiles.html
Avianca is part of Star Alliance, and thus partners with UA in the US. That
might mean easier redemption (since UA's own redemption is much better than DL's and even somewhat better than AA's), I'm not sure.
Korean is part of SkyTeam, and thus partners with DL in the US. DL itself has some of the worst redemption availability, but I don't know how it is if redeeming from Korean.
Since those two have the best expiration policies, I presume you'll want to focus on researching them further, as oppososed to continuing to consider LAN or AeroMexico?
For each, you want to look into what various ways of earning miles (shopping portals, hotel and car rental partners, etc) there are in the US, so that you complement what earning you'd get from the secured card you choose.
... And welcome to FlyerTalk,
donniegood!