Lincoln fits all four clues (unless a dragged 91+mark 4 set has ever made a public call - I don't know of such a case).
Clue 5:
Despite continual proposals, this station does not have any through services to any of the three capitals of Great Britain. It has had a through service from one of them since privatisation, but said capital is not the capital of the country it is in (so if the station is in country A, it had a through service from the capital of country B or country C).