at Lymington.

Either.

Yes, either, although 'in Lymington' is in more common usage. We tend to say "I live in Lymington, in Spencer Road, at number 29". Strange isn't it? Because surely it would be more appropriate to say "I live in number 29".

We aren’t allowed to say anything is incorrect these days, but i think ‘at Lymington’ is unidiomatic in the sentence as quoted. No one would say that X lived at London, or at Paris, surely, but may depend oddly on the size of the place?? One of those niggly things that annoy when reading.

It could be archaic. The Victorians and Edwardians (and earlier) used to use “at” so it may depend on when your book was written.
Who is the author?

I agree 'at' is usually used for name /number of actual building eg I l8ve at No 40 or at Rose cottage or at Buckingham Palace or at the museum/at the office/at tge greengrocer's. Otherwise we tend to use 'in' eg in London, in the village etc, in the countryside etc.
English is a very difficult language in some ways. I used to teach English as a second language to foreign students. They couldn't understand why you got into a car but onto a bus/train. I said it's because you have to climb up. So do you get onto a lorry they asked. No we get into it I think!
Likewise why are all garments with legs plural eg trousers, shorts, tights, culottes etc (usually singular in other languages eg un jean in French). Because tgey have 2 legs I say. But a shirt has 2 arms they reply. We also say scissors (spectacles) , glasses, tongs, shears,tweezers etc for a single item with two blades/arms We are so used to it we don't notice but confusing for foreigners.

Sorry, got a bit carried away and off topic there! Ive been thinking about this. You might say 'There' s an interesting church at x village' mightn't you?

Its Joanna Trollope- she does get a bit exact at times. Thank you for answering.

Then I think she is being pedantic or it is an elderly character in her book unless it is of her historical novels.

Ah yes, she uses some unusual constructions I seem to remember. Part of her style. It's not exactly wrong as far as I know, just not common usage.

Maybe winterwhite is correct when she suggests it's something to do with size. I hadn't considered it until now but I used to say that I lived in Ilford. Now that I've moved to a much smaller town, I say that I live at xxxxxxxxxx xxxx. No idea how this came about; there was no conscious effort on my part.

The size aspect makes sense to me, too. 'At' sounds just as natural / correct to me as 'in' if the place is village or a small town.
No, 'at' doesn't sound right with bigger places. Thinking about this, could this be because the names of bigger towns and cities frequently also refer to a whole region (with many villages or small towns within it), and off the top of my head, I can't think of any regions where 'at' would be the correct preposition. I'm not sure that I have explained myself very well, but hope that makes some sense.

Yes you wouldn't say : She lives at London , or Birmingham, but you might say: she lives at Sevenoaks, for example.

Polly, yes in French trousers and so on are singular, but they are definitely not in Danish, Dutch and German which like English talks of a pair of anything that you insert your legs or hands into.

Hebrew, both ancient and modern, has singular, dualis and plural, and if I remember correctly Classical Greek does too, which is probably why we talk about a pair of glasses, (spectacles), gloves, shoes, trousers, pants etc.

To me staying at a place as opposed to staying in it, means you are on a visit, rather than living there permanently, but this is probably Scottish usage.

Garments for legs did used to be two separate parts, once upon a time.

This is an interesting thread!

Pollyperkins - is it smaller settlements? I'm thinking of relatives' North Shropshire homes I visited as a child. In Shrewsbury, Wellington or Wem, but at Welshampton, Oswestry or Ellesmere all stir memories and somehow feel right.

Sorry Grandetante But “eine Hose” is also singular in German.

“staying” is also very commonly used in Scotland to mean “living”i.e. residing.

My grandfather came from Lymington, and he definitely lived IN Lymington.?

Our South African relatives call swimming trunks 'a Speedo'!

Maybe if she lives near Lymington, she is living "at" not "in"?

Oops, yes of course die Hose is singular! What was I thinking?