Wirelessly posted (BlackBerry8530/5.0.0.601 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)

"I wonder if we could do LAX-Lima-Quito for the Galapagos and Machu Picchu, can we elegantly get back from Quito-LAX on LAN? Is either BA or AA better for booking flights on LAN? Could we somehow fly LAX to Thailand with Hawaii as a stopover? If we decided on Ireland and UK. are we better off flying LAX to London to Dublin on BA or should we fly through Dublin on a partner to avoid BA taxes? Spain is best on Iberia, I assume?"

I think that LAN's only nonstop out of LAX is to LIM, so if you use BA miles for an all-LAN routing, you would have to route through LIM. If you want stopovers in South America, use BA miles: AA All-Partner awards do not permit free stopovers in South America. If you do not need a South America stopover on the way back, you could redeem BA miles going, and AA miles returning (perhaps returning via MIA). Or, if you redeem AA miles for UIO-LIM-LAX on LAN, you might be able to append a free one-way from LAX to Hawaii on the same award, for travel months later. As noted, LAN now flies between GPS and GYE/UIO, but getting award seats on that route might be difficult.

For travel to MAD, there is IB's nonstop from LAX, but there are also other routings possible, combining AA and IB, with connections in the U.S. and/or in Europe.

AA has seasonal service to DUB from ORD; a connection through MAD on IB is also possible.

In theory, an AA award LAX-HNL-Japan-BKK, with a "gateway" stopover in HNL, might be possible, depending on whether JL has a published fare allowing such a routing. AA can advise you on that.