In chapter 13 (Deep Magic from the Dawn of Time) of The Lion, the Witch, and the Wardrobe, Jadis claimed that a traitor's life belong to her, but nothing was said about it in The Magician's Nephew, the book about the creation of Narnia, nor of the stone table.
Quote from The Lion, the Witch, and The Wardrobe:
"Have you forgotten the Deep Magic?" asked the Witch.
"Let us say I have forgotten it," answered Aslan gravely. "Tell us of this Deep Magic."
"Tell you?" said the Witch, her voice growing suddenly shriller. "Tell you what is written on that very Table of Stone which stands beside us? Tell you what is written in letters deep as a spear is long on the trunk of the World Ash Tree? Tell you what is engraved on the sceptre of the Emperor-Beyond-the-Sea? You at least know the magic which the Emperor put into Narnia at the very beginning. You know that every traitor belongs to me as my lawful prey and that for every treachery I have a right to a kill."
"Oh," said Mr. Beaver. "So that's how you came to imagine yourself a Queen—because you were the Emperor's hangman. I see."
"Peace, Beaver," said Aslan, with a very low growl.
"And so," continued the Witch, "that human creature is mine. His life is forfeit to me. His blood is my property."
"Come and take it then," said the Bull with the man's head in a great bellowing voice.
"Fool," said the Witch with a savage smile that was almost a snarl, "do you really think your master can rob me of my rights by mere force? He knows the Deep Magic better than that. He knows that unless I have blood as the Law says all Narnia will be overturned and perish in fire and water."
"It is very true," said Aslan; "I do not deny it."
"Oh, Aslan!" whispered Susan in the Lion's ear, "can't we—I mean, you won't, will you? Can't we do something about the Deep Magic? Isn't there something you can work against it?"
"Work against the Emperor's magic?" said Aslan turning to her with something like a frown on his face. And nobody ever made that suggestion to him again.
And later, after Aslan came back to life, here's Aslan's explanation about the Deeper Magic:
"It means," said Aslan, "that though the Witch knew the Deep Magic, there is a magic deeper still which she did not know. Her knowledge goes back only to the dawn of Time. But if she could have looked a little further back, into the stillness and the darkness before Time dawned, she would have read there a different incantation. She would have known that when a willing victim who had committed no treachery was killed in a traitor's stead, the Table would crack and Death itself would start working backwards.
Now in The Magician's Nephew, we learned that Jadis did come into Narnia at the dawn of Time, not before it. The book, however, didn't mention any "contract" drawn between Jadis and Aslan, or between Jadis and the Emperor-Beyond-The-Sea.
Is the reader supposed to assume that the Emperor or Aslan made the agreement with Jadis to apply to any world because Jadis didn't seem to know about Narnia's existence until she stumbled into it along with Digory, etc. from the "Wood between the Worlds"?
Did C.S. Lewis explained this in any of his letters, in another Narnia book, in an interview, or in his other writings?