Thanks for your help so far, Darren and Number_6!

I checked with my friend again, the detailed itinerary is this:
LHR-HKG (BA)
HKG-BKK (CX)
BKK-SIN (QF)
SIN-DPS (QF)
DPS-DRW (QF)
DRW-PER (QF)
PER-MEL (QF)
MEL-AKL (QF)
AKL-SCL (QF)
SCL-EZE (BA)
EZE-GRU (BA)
GRU-GIG (BA)
GIG-LHR (BA)
All flights seem to have been booked into K class.

So I take it LA would be the best program for this itinerary?