The LOTGK says she "salutes" the giants which suggests they either outrank her in power or are equally powerful in their own realms.

"salute" at its simplest means greet. 

Lewis uses its medieval meaning, which can involve a kiss of greeting, as well as a mark of respect. It comes from Latin word, which has a suggestion of wishing the person good health. 

The LOTGK has a good relationship with giants, and perhaps she addresses them in a respectful way, but I doubt she has respect for them.

...Ok I know this theory has already been addressed and dismissed, but I do have a personal soft spot for the possibility that she's Jadis' daughter, taking revenge for her mother. As to who would be willing to have a child with an ice witch - Jadis is repeatedly said to be beautiful, and also I could see many evil-alligned creatures caring more about sucking up to power than having a *good* mate?

Another possibility I would be willing to accept, re: her and Jadis being of "the same crew", is the possibility that Jadis trained and indoctrinated a cult of witches of other species origins while she was in the North, and LOTGK is the last survivor or descendant of this cult.

Another thought I've run into that I find amusing, although less resonant than the previous possibilities, is that LOTGK is actually snakey rather than humanoid by her birth nature, and a witch took her in as a familiar/assistant and taught her to shapeshift.

@silverlily Interesting ideas! I don't think it's completely "against canon" that the Green Witch could be a family relation of Jadis — it's just that they couldn't be the same person, going by what we know from the books. But "one of the same crew" could very well mean they are literally related. Going by the very little we know, it's not outside the realms of possibility that Jadis could have had a daughter, perhaps fathered by one of the other evil creatures she may have met during her time in the North before she re-invaded Narnia as the White Witch. Maybe the Green Witch's father was also a humanoid who could turn into a snake, or a snake who could turn into a humanoid...

Or else (given the stretch of over 1,300 years between Jadis's final defeat in LWW and the Green Witch's reign in SC), maybe the Green Witch could be a later descendant — a granddaughter or further down — since we don't know whether she herself was immortal in the way Jadis became after eating the apple. But again, there's nothing to suggest they couldn't have been related "by blood", or that they didn't know each other in the distant past, if the Green Witch was also immortal (unless killed in battle) or at least very long-lived.

Posted by: @silverlily

Another thought I've run into that I find amusing, although less resonant than the previous possibilities, is that LOTGK is actually snakey rather than humanoid by her birth nature, and a witch took her in as a familiar/assistant and taught her to shapeshift.

I'd never thought of that idea, but I reckon it's not outside the bounds of possibility either! I sometimes wish Lewis himself was still around for us to bounce all these questions off him and I wonder what he'd say — hopefully something more interesting than "Oh, gosh, even I don't know — I never thought about it that far myself..."   (He was very happy to answer young fans' questions about Narnia when they wrote to him during his lifetime, and there's a book of his letters to children, but unfortunately I don't think any of them deal with this particular question!)

@spalatin-rengriss 

Came on this looking for anyone that noticed the connection between the Lady of the Green Kirtle and Morgan Le Fay.   It hit me when reading "Connecticut Yankee in King Arthur's Court" a book in Lewis's library.   What struct me initially was the contrast between her beauty and sweetness of personality and her evil nature.  But also they are both trilling and musical.   Here's the passages from Connecticut Yankee: 

To my surprise she was beautiful ; black thoughts had failed to make her expression repulsive, age had failed to wrinkle her satin skin or mar its bloomy freshness. She could have passed for old Urien's grand-daughter, she could have been mistaken for sister to her own son.
...
But Morgan was the main attraction, the conspicuous personality here; she was head chief of this household, that was plain. She caused us to be seated, and then she began, with all manner of pretty graces and graciousnesses, to ask me questions. Dear me, it was like a bird or a flute, or something, talking. I felt persuaded that this woman must have been misrepresented, lied about. She trilled along, and trilled along, and presently a handsome young page, clothed like the rainbow, and as easy and undulatory of movement as a wave, came with something on a golden salver, and kneeling to present it to her, overdid his graces and lost his balance, and so fell lightly against her knee. She slipped a dirk into him in as matter-of-course a way as another person would have harpooned a rat !

Poor child, he slumped to the floor, twisted his silken limbs in one great straining contortion of pain, and was dead. Out of the old king was wrung an involuntary " O-h !" of compassion. The look he got, made him cut it suddenly short and not put any more hyphens in it. Sir Uwaine, at a sign from his mother, went to the ante-room and called some servants, and meanwhile madame went rippling sweetly along with her talk.
...
Morgan le Fay rippled along as musically as ever. Marvellous woman.

Since Lewis was influenced by the King Arthur stories it is very likely that he would create characters that were based on those in the legends of Arthur and works of literature which contained similar stories such as Spenser’s Faerie Queene.  Morgan Le Fay would be an interesting character to base a witch on, and she was quite similar to the Lady of the Green Kirtle. The King Arthur stories have much in common with medieval Narnia. I think the character of the Lady worked very well in The Silver Chair. 🙂

Do people still read Mallory’s Le Morte d’ Arthur and Spenser’s Faerie Queen?  I think English majors in colleges and universities still read it, but it is no longer required reading for the basic courses in liberal arts institutions. So chances are that many people living here in the U. S. may not even know who Morgan Le Fay was.  It is kind of unfortunate that people’s knowledge of literature is rather poor, but it is the time we live in. They would know that the Lady of the Green Kirtle was a witch, but they may not make the connection with the medieval stories of King Arthur.  C. S. Lewis would have thought our culture is sadly lacking in its understanding of mythology. 🙁

I recently discovered another likely inspiration for LOTGK... this has apparently been mentioned on the forum in the (somewhat distant) past when the naming contest for the Lady was happening. 

I actually came across this painting:

https://www.google.com/search?q=lamia+painting&client=ms-android-samsung-rvo1&sca_esv=68b5c75d01228b39&ei=aum5ZvqKBanhwN4PwNqBWA&oq=lamia+paintinf&gs_lp=EhNtb2JpbGUtZ3dzLXdpei1zZXJwIg5sYW1pYSBwYWludGluZioCCAAyBxAAGIAEGA0yCBAAGAUYDRgeMgcQIRigARgKMgcQIRigARgKMgsQABiABBiGAxiKBTILEAAYgAQYhgMYigUyCxAAGIAEGIYDGIoFMgsQABiABBiGAxiKBUjUK1DSDliwJ3AAeACQAQCYAd8CoAH6C6oBCDExLjIuMC4xuAEByAEA-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&sclient=mobile-gws-wiz-serp#vhid=KhdwdlWwBC4K_M&vssid=_cem5Zq2qG-7jwN4Pgc_q8Ag_39

It shows a young knight being wooed by a lady in a garden... and if you look closely you'll see a recently-shed snakeskin on the ground, ominously hinting what this lady has been up to. The painting, by John Waterhouse, depicts the Greek tale of Lamia, a half-woman, half-snake entity said to ensnare heedless young men with her false beauty before turning into a serpent and preying upon them.The painting itself is inspired by John Keat's poem, also entitled Lamia, which Lewis was almost certainly familiar with (he apparently was such a fan of Keats he had been heard to shout at a student who disliked him: "If you think that way about Keats you needn't come here again!").

While I still think Error from The Faerie Queene had something to do with Lewis' inspiration here, this seems like a very direct influence. The imagery of the painting could practically be an illustration from the Silver Chair (although Lamia should admittedly be wearing green), and the poem is definitely in Lewis' wheelhouse.

A proposal.

The Lady is a Salamander of Bism. She later studied magic and learned to acquire humanoid form.

She cursed Puddleglum to boil his blood with fire in his veins. She used a "scorching" voice.

In her serpent form, her eyes actually looked like fire.

When enraged, she reverted to a serpent instead of a third shape that might have succeeded, such as a giant. The most capable Evil Overlords know: "I will not turn into a snake. It never helps."

(#34, if you're curious. http://www.eviloverlord.com/lists/overlord.html )

Only the inhabitants of Bism know that Bism exists. (Aside from Aslan, of course.)

She conquered them first. This suggests she was familiar with them.

As for the actual Salamanders:

The Earthmen described them as sentient and "eloquent," and admired them.

They speak in a "scorching" voice.

The Salamanders were described as "like" small dragons, but not that they actually were small dragons.They are a separate species.

In most mythologies, dragons and their lookalikes are impervious to age or illness i.e., more or less immortal (unless they are killed).

As to the Underworld:

The heroes assume that the Lady cast a curse upon her realm that it would be destroyed if she died. Instead I propose that she cast spells while alive to press back the sea and to expose dry land. Then her captives would have a place to build her city. When she died, those spells dissolved and the sea returned to its original seabed.

(If our world can push back the sea in the Netherlands without magic, I expect the Lady certainly could do it.)

As to why the Lady chose to become evil:

Who the heck knows? As a Terminator once said, "It's in your nature to destroy yourselves." Sometimes people just do the wrong thing.

See, this is one of those questions - and if you've been a fan of Narnia for as long as I have, you know there are so many of these questions - where the short answer is "Lewis doesn't tell us".  I was just reading over on another thread, where we were talking about how the four Pevensie kids went back to being kids after returning to our world.. and someone basically used that as their answer to a comment I made.  "Lewis doesn't tell us" is always the only technically correct answer in those places.

But here's the thing: discussions like this remind me of something an instructor said in a writing course I took: "Readers love to play detective".  So while yes, officially, the only canon-whatever answer is "we don't know"... we like to talk about what we do know and see what comes out.  And personally, as long as we don't try to put words in Lewis' mouth, I find that kind of fun.

So, returning to the Lady of the Green Kirtle... yeah, we know surprisingly little about her.  From a simple question like "who is she" to cooler and more interesting things like her motivations, strategies and so on.  She could have been anybody, and I agree with @icarus about Star Wars trying too hard to connect new characters to old ones.  Staying on topic though... she could have been a friend of Rillian's mother, who did something wrong and got herself exiled; she could have been a monster from Bism or below Bism; she could have been someone possessed by the White Witch (which to me makes a lot of sense from a symbolism standpoint, tho IMO that type of thing would have been better in LB).  But who she is... yeah, the correct answer is, we do't know.  And without knowing who or what she is, figuring out her motivations would be hard.  I kind of like my monster from Bism idea, because then her reason for choosing to attack from underground would make a little more sense (well, more sense than finding her way to Bism, enslaving all the gnomes somehow, bringing them up higher, having them build a city, and so on).  But yeah, the correct answer is "we have no idea".

But in this case, I think that's okay.  Part of what made her such a cool character is that she was such a total wild card.  Everything about her, even her name, is a mystery.  And I'm okay with that.  🙂

Even what Lewis tells us in the book, doesn't really explain much.

[...] Prince Rilian was talking over the whole adventure with the older and wiser Beasts and Dwarfs. And now they all saw what it meant; how a wicked Witch (doubtless the same kind as that White Witch who had brought the Great Winter on Narnia long ago) had contrived the whole thing, first killing Rilian's mother and enchanting Rilian himself.

[...] they saw how she was in league and friendship with the dangerous giants of Harfang. "And the lesson of it all is, your Highness," said the oldest Dwarf, "that those Northern Witches always mean the same thing, but in every age they have a different plan for getting it."

(Silver Chair) (my emphasis)

Old and wise Beasts and Dwarves can only say that she belongs to a kind of witches (Northern Witches) that seem to make new attacks (with new attackers, no reincarnations) in every age, using always new plans. But no distinguishing descriptions of these witches are given. We can make our own fanciful guesses, or just live with the mystery.

@cleander 

and if you look closely you'll see a recently-shed snakeskin on the ground, ominously hinting what this lady has been up to.

I thought that snakeskin was the intricate patterned piece of cloth draped modestly over her knees in the picture.   Though the painting might be a valid inspiration for LOTGK, the trouble is that the Lamia picture's barely visible clothing is too pink & too scanty to be mistaken for a green kirtle, normally worn in autumn climes, and which we discussed about a decade ago on Narnia Web, when we thought that Silver Chair was going to be the next Walden picture. 

@The Old Maid

A proposal.

The Lady is a Salamander of Bism. She later studied magic and learned to acquire humanoid form.

She cursed Puddleglum to boil his blood with fire in his veins. She used a "scorching" voice.

In her serpent form, her eyes actually looked like fire.

Now that is an interesting idea. Especially as once she turned into a snake, LOTGK seemed somewhat less articulate than she was as a woman.

One more proposal. Why would she invade and conquer Narnia?

If she did it for her own purposes, it's still a mystery as to what purpose would be served. Her existing realm was strong and stable. To attempt more could over-extend her personal and military abilities.

But the "Gentle" Giants of Harfang certainly would gain from her actions. To coin a phrase, they live in a land of Magnificent Desolation: stark beauty, if you're a geologist.

But unless they have greenhouses or an express road to the sea, they have no food.

With a witch as their neighbor, they could eat all the prisoners she sends them.

Plus, they could conquer the backwards Giants and claim Ettinsmoor for themselves. The inhabitants would be caught between the two aggressors and probably eliminated. That land provided plenty of food for Puddleglum and the children. The Harfang nation would benefit from such an expansion.

...

As for the Lady's actress, I would have stepped through a time portal to choose Catherine Zeta-Jones.

[EDIT: Several images. One picture is a green dress. Well, a sea-foam green dress, closest I could find.]