You can try, but CX is quite strict at protecting lounge access now ... they live up 100% to the rules, but also expect you to do the same. This means you must have a OW ticket to get access legally. A supervisor can make an exception, but the personnel at the door cannot. I was in this situation in April in HKG (flown CX in F arriving into HKG and then left on SQ in F the next day). The SQ F lounge was so bad that I went over to the CX lounge and begged for access. It was an ordeal, and only granted as I had with me 4 F boarding pass stubs for travel on CX in the past 2 weeks. The supervisor was gracious, but made a point of saying that this was a very exceptional privilege (to be allowed into the lounge when not flying OW that day) and I should not expect it to happen routinely unless I were Diamond (CX's FF plan top level). Probably that was a hint to join CX's plan (which I have not done, I am sticking with AA and QF for now).