Caroline

She lived in the same village and attended the same church as the Herritons... no blood relationship. She befriended Lilia and accompanied her to Italy as a favor to Mrs. Herriton - but Caroline was not very successful in keeping Lilia out of trouble.

I was also totally unclear about this. In fact, by the end, I was still wondering what was the point of this character to the story. She seemed to be quite incidental in every sense, and that sometimes made her presence a little jarring to the narrative.
Beautiful performance by HBC though, as always.