In "Lamb to the Slaughter," what do you think Patrick would have written to his brother before he left work on the fateful day?

Very interesting idea! Of course, what goes to the heart
of this question is what Dahl is very careful not to reveal: the reason why Patrick is
going to leave Mary. We as readers are left to guess at the reason, but I think there
are definite clues in the text that point at guilt on Patrick's part. Note the following
description:

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He had now become absolutely motionless, and he
kept his head down so that the light from the lamp beside him fell across the upper part
of his face, leaving the chin and mouth in shadow. she noticed there was a little muscle
moving near the corner of his left
eye.

The nervous tic
mentioned and the way he is keeping his face partially in shadow indicates that he is
very guilty about what he is about to do and wants to hide himself as he tells Mary that
he is going to leave her.

I think therefore that if he were
to write a letter to his brother that morning, it would explain his decision to leave
Mary and give the reason why. The most likely guess to my mind is that he has met
another woman who is more exciting and interesting than Mary. Perhaps Patrick got tired
of how obsessed Mary was with him - she certainly is described as being the model of a
loving and an affectionate wife, which is perhaps what Patrick did not want. We can only
guess, but his letter would, I think, express his feelings of guilt at leaving
Mary.