I see your point, and actually I originally had some comments about that possible reading, i.e., it could be interpreted as being the *lounge* between the flights, rather than the connection between.

However, I ultimately dismissed that interpretation because it seems to me that would render the "vice versa" meaningless.

​​​​You wouldn't need to include the vice versa case of SH Y to LH J as qualifying, because if they were referring to the "in between" lounge, there would always be access to that lounge by virtue of the departing J flight.

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PS, unfortunately the graphics have been broken on that thread and others for some time.