> somebody called Phillips Barry in the early 20th century,

Barry (1880 - 1937) was a prominent American folksong collector and scholar.

What made Lloyd so partial to the name "St. James's Hospital"? Because it would make the song sound "medieval"?

One can't defend Lloyd's misleading frequent custom of failing to mention that he'd tinkered with words or tunes. On the other hand, his revised versions and his performance of them are very skillful and seem to retain the spirit of the originals. (Though in one case there seems not to have been an original.)