I say, steady on old chap !
Why didn't he like him? Well, for one thing, the playboy prince didn't fit what Lang thought the King and Emperor should be and was not his type at all. Lang was a reactionary bound by what he thought proper, in an age marked by 'correct' standards rather different from ours, an age when divorced people weren't allowed in the Royal Enclosure at Ascot. It's difficult to put ourselves back in those times and accept that way of thinking.
His oath of loyalty was, to him, of loyalty to the monarchy rather more than to someone whom he was convinced was not fit to be its representative. That he was a devious individual, and 'traitorous', doesn't mean he wasn't sincere and well-meaning.
Mind, had the King stayed King, it's not certain that he would have proved, with his consort, a better monarch than his successor, with his wife, proved to be.