In Ch. 23 offering to help Lucy roll the paper to finish Annamaria's filigree (or fillagree or filagree--so many alternative spellings) basket, provides Elinor the opportunity she seeks to renew the subject of Lucy and Edward's engagement and--I guess--to prove that she is quite composed on the subject.

They are making this of paper, but 'real' filigree is done with gold and silver. The kind of work Lucy (and Elinor) are doing is also called quilling.

Here are a few links to show what it looks like and explain how it's done:

Scroll down to the picture of the basket

Another example, but a Russian style

Explains the history of quilling and how it is done

Another explanation

Shows some flowers and types of decoration

From these pictures, you can imagine how this would appeal to a little girl!

Some other looking around I did online mentions that the craft has existed since the middle agesand was very popular among fashionable ladies in the 18th and 19th centuries. This is no doubt part of the appeal for Lady Middleton, although she would not exert herself to do it herself! (the other part of the appeal being the over-indulgence of her child, of course)

But here's something that really caught my interest: As I was looking for some links to post here, I happened upon an online dictionary which gives, as its second meaning for 'filigree'

Fanciful; unsubstantial; merely decorative. (because real filigree is not made of paper)

And it made me wonder--was Jane Austen using this symbolically? I doubt it's a coincidence, and it suits Lucy. If you think about the filigree baskets, they are very pretty to look at, but would have no functional purpose other than that. They wouldn't be able to hold or carry anything...