I have few problems trying to access other OW lounges, provided I have been flying a OW carrier that day.
HKG (Wing) and MEL both fine (agree with other posters, CX couldn't have been nicer letting us in, almost felt guilty eating the Balik salmon!)
Never had a problem with access to BA lounges, but maybe this has been because I have either been flying BA, or have been on a OW flight code-sharing with BA (eg flying BA flight number on IB, used IB lounges).
Interesting issue in ORD however. Was flying with BA and so had access to both the F and J lounges, but being in Y, no access to the pre-flight dining. The food offerings in the F lounge were almnost non-existant (bag of crisps and dry sandwich), and only crisps in the J lounge.
Walked over to the EI lounge (flight had just departed and door was closed) - the entry staff were just shutting off the computers and saw me, came and asked me what I wanted - I explained the 'no food' situation and so the invited me in, took me to the kitchen where all the food had just been returned and told me to 'knock myself out'.
Left lounge with three or four delicious sandwiches and other nibbles. Even offered me a (real) plate to put it all on! ^
Nice EI.
Regards
L/M/E FF