I can think of three reasons why they don't do as you suggest;

1. CX don't want those QF/BA customers (that can't access the Wing/Pier using OW) in their lounge.

2. QF/BA don't want their customers in the lounge showing what a far superior product CX have - they may even think about "trying" them out in the air.

3. Cost - With 2 or 3 departures to LHR a night for BA, the upcoming QF flights to LHR ex HKG and the 3+ QF/AO departures a night, that is a decent volume of pax in an 8 hour period, it might actually be cost efficient having your own lounge.

and to be frank, CX is not really that close with BA or QF. Just look at the little number of codeshares between CX and these two airlines - there aren't that many.