There is a rumour that CX will have an arrival lounge in HKG in September:
http://www.flyertalk.com/forum/showthread.php?t=843144
But some sources said that the lounge will be for F and OW-EM/SA passengers on CX/KA flights only. If that is the case, you may not be able to use the arrival lounge.
There is a paid-in lounge - Plaza Premium Arrival Lounge. I have never been there. I do not know if this is the same one as the rumoured CX arrival lounge. If so, this lounge may not exist after the CX lounge opens.