This is from the CX UK site, but gives details of what you can access
http://www.cathaypacific.com/cx/en_G...tails.HKG.html
As
djibouti mentions, only the Wing has an F/OWE section (the Pier does also, but looks like it's closed currently), so you can access several lounges in HKG.
Haven't been through LAX for a while, so can't advise on that.