Chances are that the paper is either filled with gibberish or that it remains a blank paper. Lady Macbeth's sleepwalking is caused by the guilt she carries for her part in the murder of Duncan as well as the other murders that have taken place in the play. In her sleepwalking, she is reliving bits of related experiences. It's possible she is using the blank paper to write a reply to the ill-fated message Macbeth sends her in Act 1.
Gentlewoman: I have seen her rise from her bed, throw her night-gown upon her, unlock her closet, take forth paper, fold it, write upon't, read it, afterwards seal it, and again return to bed... (5.1)
In Act 1, scene 5, Lady Macbeth receives Macbeth's letter telling her what the witches told him in scene 3. She decides that she and Macbeth will do whatever it takes to make him become king--including killing Duncan. She asks the spirits to fill her with cruelty and to make her strong and masculine so that she can commit murder. She seems to have no problems with this strength until it comes to dealing with the guilt.
If Lady Macbeth is actually writing anything at all, it may well be a confession because her words from the sleepwalking scene amount to a confession to those listening even though what she is doing is reliving bits of what went before and remarking on her continuing experiences (not actually confessing).
Lady Macbeth: ...Fie, my
lord, fie! a soldier, and afeard? What need we
fear who knows it, when none can call our power to account?--Yet who would have thought the old man to have had so much blood in him. (5.i)