With the exception of the LHR Clubhouse, as long as there is a lounge that is actually operated by a Skyteam member (and not a 3rd party operator), you will have access as STE+ on an interrnational Skyteam flight. You will also have access to the joint Skyteam lounges. Yes, the 3rd party operated lounges are going to be hit and miss at times depending on contractual relationship unless you are flying in Business Class. Although the Skyteam lounge finder is not updated that frequently and may have errors. Generally speaking, if you are flying one of the Skyteam partners that has a contractual relationship with a 3rd party lounge, you should get access as a STE+ member (as long as you are not a DL STE+ member -- see below).

The situation for Delta STE+ is more restrictive as we do not get access to any 3rd party operated lounges when flying on DL metal internationally unless flying in D1 business class (as DL is able to be more selective with lounge entrance rules for it's own elite members). Further, DL eliminated DL Sky Club access to DL STE+ members on international flights unless flying in a Premium Economy Skyteam cabin. Partner STE+ continue to receive DL Sky Club access when flying international (with exception of Caribbean) flights in any Skyteam cabin.

Note that neither DL STE+, nor partner STE+, get DL Sky Club access on purely domestic US itins.