I will be taking my 3d and 4th F trips on LA soon. It is VERY difficult to score anything but a full F seat. I have been on flights (2, in fact) where I have had to check frequently for an award seat, then finally ONE will open up, and I am the only passenger seated in F. Don't forget that the F cabin only has 5 seats total (one row of peace and quiet sleeper seats where curtains do not pose any threat to anyone's national security.) What particular city pair are you trying to fly through? Also, there may be some availability with a connection in LIM (but really, you want to avoid that if possible).