Just to concur,
Check in opens around 3 hours before the first flight - they both leave about 11pm.
Qantas Lounge OK.
Cathay Wing much better. I'd go there. Gate 1-4. Come out Security from the side which you will use having checked with BA and turn left and keep going. You need to go down one level unless you have a Gold card with BA. It is a about a 10 minute walk but its the best lounge.
The Pier is near gate 65 which is also good (only business class there - the Wing has a First section).
That is my view. Done it many times!
FD.