IN GENERAL: For US-based lines, you get access to their lounges with an international (including Canada) boarding card and an alliance card such as Star Alliance Gold or OneWorld Sapphire, and this is always posted for you and ONE guest. This is better treatment than they give their own status flyers. As you noted, US, and also AA do not give lounge access with either status or domestic First. Lounge access is usually restricted to purchased membership in the RCC or Admirals Club for example. If you have a purchased membership such as these, you are then allowed to bring in the complete (immediate) family, or one non-family guest.

In some airports when flying J, AC has arrangements with other carriers, such as the private lounge in MIA or a wonderful little Continental lounge in SFO. I have never seen a published list of these, or their rules.

Things are a bit more generous this side of the border. MLL lounges are open to US-based Star Alliance status members on much the same rules as they grant us, but AC Elite and up get full access (including all family members) with no need to purchase membership. Class of service, of course always gets access too, unlike US lounges. Mind you, MLL also now allow Latitude, Amex, and assorted hangers-on in!

It is fairly simple, and has basically been this way for a long time. One reason why I always got OW status in the Good Old Days with CP rather than AA, and now stick with AE rather than MP.

Those are the basics AFIK. International airports are a lot more complicated varying in my experience airline by airline and airport by airport.

E&OE, please feel free to point out my over-simplification, but the above has usually stood me well when trying to bluff a Lounge Dragon Lady.