What would be a good thesis to write about "The Necklace" including examples from the passage and answering the question "is lying ever the appropriate behavior"?
You are going to need to choose a side. If you choose the positive side, your thesis should be something like this.
Lying is appropriate behavior when it is intended to prevent someone else from harm.
You could argue, for example, that Madame Forestier did not tell Mathilde that the necklace was a fake because she wanted her friend to feel valuable and enjoy herself at the party. It is true, she had a good time.
Madame Loisel was a great success. She was prettier than any other woman present, elegant, graceful, smiling and wild with joy. (p. 4)
Perhaps Mathilde did not tell her friend that she lost the necklace because they were very old friends, and she did not want Madame Forestier to be mad.
The other thesis is the opposite.
Lying is never appropriate behavior because it can have unintended consequences.
Mathilde’s friend Madame Forestier did not tell her when the necklace was returned because it was late, and Forestier was annoyed
Madame Forestier, deeply moved, took her hands. (p. 7)
Yet Madame Forestier’s lie basically ruined Mathilde’s life. She spent ten years trying to replace a fake necklace with a real one. If Madame Forestier had told the truth, either when Mathilde was looking at the necklace or when she returned it, much hardship could have been avoided.
The other side of the coin is that Mathilde brought it on herself because she lied and said she brought back the necklace when she really replaced it.
"Yes. You never noticed it, then! They were very similar."
And she smiled with a joy that was at once proud and ingenuous. (p. 7)
If Mathilde had not been so prideful, she would have saved herself and her husband a lot of grief. The necklace was not real, so it was worth hardly anything. She could have easily replaced it.