A ticket paid for with miles (or part miles part money) is no different from one paid for entirely for money in terms of the lounge access policies of CX or OneWorld (there is, in general, no way another OW lounge could tell the difference - if you have a J boarding pass then that's good enough). You would normally get a lounge invitation card from CX, but even if you don't you can still access the lounges. Note that you may not get access to some OW lounges which are operated by 3rd parties if you are not flying on the OW airline in question.

The one exception is if you get a free operational upgrade at check-in - with those the check-in staff often mark the boarding pass to that effect and you will not then get lounge access.