I was finally able to book my AONE3 on-line. I did it as an ex-ICN (Korea) itinerary.

I had to get the oneworld desk involved to get it done.

The problem, and the reason I was getting the error message, was that the tool showed one of the Cathay flights as available in F (LHR to HKG), but it apparently wasn't so the tool locked-up and gave me an error message (without telling me what the error really was).

I switched the flight to BA and was able to book it. I then went to the CX office and switched it back to the CX flight, which was in fact available.

There is a problem in that CX uses a proprietary internal booking engine. The availability showing elsewhere does not always match. For example, Apollo showed it as A4. Sabre showed it as A0.

I have run into this with CX in the past.