When you change the way you look at things, the things you look at change.
If Lublin was occupied then the unit would negate it's own hex's EZOC and supply could pass through. If unoccupied, even though the space is controlled, I assume the EZOC would block the supply chain from passing through the city.
Is this right?
I presume that if Lublin is occupied by a "friendly" unit it would negate EZOC, then YES it is "In Supply".
Lublin ITSELF (I think) is in supply as it can trace it's own supply to the edge of the board...the EZOC doesn't affect the city (or in fact any unit, either) that you have designated to check for supply. You start the trace in an ADJACENT hex. So you could potentially have the case where a (non-fortified) city is in supply but not part of the supply network.
I'm not sure what you are saying here.
Lublin would be "In Supply" as long as there is no EZOC in your path.
Hope that helps.