You seem to be confusing whose miles you have with whose airline you want to travel.

If you have AA miles, you are using AA's award chart to fly on LAN and it is irrelevant what LAN charges their members for that flight. Since AA.com doesn't show LAN award availability, you would have to call AA for availability and remind them to waive the phone booking fee since you can't book online.

You might find this thread useful: http://www.flyertalk.com/forum/ameri...-aa-miles.html