Granted, I have never flown Lan Ecuador, so I am not speaking from experience, but aa.com lists only LanChile and LanPeru under the Lan umbrella of eligible, miles earning tickets.

"Earn a minimum of 500 AAdvantageŽ miles each time you purchase and fly on a published eligible fare ticket on LanChile (including LanPeru), a member of oneworld."

Given this information, it seems like LanEcuador flights are not eligible...something I was not previously aware of.