Meaning of "take down" in "I met her at some dinner and took her down."

I've encountered this particular use in Greville Fane (1893) on two different occasions and am quite perplexed by the actual meaning as none of the meanings for that idiom given by the dictionary seem to fit very well:

1. I spoke of her to the lady I had taken down, but the lady I had taken down had never heard of Greville Fane.
2. I met her at some dinner and took her down, rather flattered at offering my arm to a celebrity.

The idiom dictionary lists 2 seemingly relevant uses:

1. To lower someone's arrogance or self-esteem: The opposing team really took him down during the final game. They were so good that they took down each member of our debate team.
2. To write something one has heard or observed: I took down every word they said so I could review the conversation later. The stenographer took the speech down and transcribed it.

1) does not seem to fit the meaning. There seems to be no malice in the speaker's words, and he stated that he "liked" one of the persons that were "taken down" by him.

2) seems like it could fit. The narrator is a journalist, so I can guess that "taking down somebody" could mean interviewing that person, but I'm really unsure, as no example in any dictionary backs up my theory. All examples I could find are similar and mention "taking down" something like a speech or a conversation.

This is a separate meaning of the phrasal verb take down, one which is now fairly old-fashioned.

This sense doesn’t seem to be included in many standard dictionaries: Merriam-Webster, American Heritage, and Oxford Dictionaries Online all show no trace of it, and as you mention, nor does The Free Dictionary.

The OED article on take, however, does include it, as sense 8 of the phrasal verb take down:

trans. Of a man: to escort (a female guest) into dinner. Now arch.

1887   Mrs. J. H. Perks, From Heather Hills, II. xviii. 308
      A quiet dinner-party, with a nice, sensible man to take you down.

There are a few other quotes as well, but this one best illustrates the meaning, I think. Quite noteworthy, though: although the article labels this usage archaic and most of the quotes are from the 1800s, the most recent quote is from Jane Feather’s 2011 (!) novel A Wedding Wager, so it is still occasionally used.

While I have no evidence to back this up, my intuitive understanding of the verb is that down here is in essence meant literally: in traditional houses, especially the upper-class settings in the UK where such dinner parties would frequently occur in the 19th century, the dining room or dining hall was located downstairs, while the rooms that people stayed in were upstairs. If you read novels of the time, you will almost invariably see people coming down for breakfast or dinner, and this did literally include walking down the stairs at the time. If a gentlemen were to escort a lady to dinner, they would likely meet on the landing or in the hallways upstairs, and then go down the stairs together.