As a Plat, you have access to OneWorld Business Clubs... check the list
http://www.oneworld.com/ow/ffp/lounge-access/search
at HKG... there seem to be 3 CX Business Class lounges, a BA/QF and also a JAL lounge...
At LAX, since you are flying CX, you can access the British Airways, Cathay Pacific and Qantas Joint Lounges (First and Business Class)
you might want to Priceline a hotel at HLG if you want to sleep... or just lounge hop, or even head into the city for a few hours...
