Number one is to make sure his Qantas Club membership number is already applied to his reservation. This can be done by calling Qantas reservations and asking. If his number is in the booking, then it will be printed on his boarding pass.

Priority checkin should not be a problem as his status/membership will show up on the reservation at the checkin desk. If anyone tries to check his status before he reaches the checkin counter, its probably best to be able to show a recent boarding pass that also has his Qantas Club membership number printed.

The BA lounge at Heathrow is notorious for their desk agents wanting to actually see the card even though the status and membership number are printed on the BA-issued baording pass. He may need to show is "copy" of the card (a photocopy I assume) and it might even help if he has a copy of the police report from when his wallet was reported missing. I doubt an agent will deny access with such "supporting evidence". The main thing the BA agents seem to be looking for is whether the membership is still valid or has expired, hence they want to see the card and check the expiry date. If that is clearly shown on the photocopy then it should not be a problem.

Of course Qantas charge a fee to re-issue the card and it takes some time so probably easier done upon return to Australia. He may be able to claim the re-issue cost on his travel insurance policy along with other costs incured from the lost wallet. But the insurance company are going to want the police report as well!