How should I go about writing a scene based on Lady Macbeth that has a soliloquy and falls between Act 4, Scene 3 and Act 5, Scene 1 of Shakespeare's Macbeth?

This is a fascinating spot in the play to add another scene with Lady Macbeth. Some people feel this is a section which may have lost a few scenes over the course of time.
We last see her as she watches Macbeth face Banquo’s ghost. She sees nothing, of course, and makes excuses to the noblemen. Her life is crumbling around her. When she next appears on stage, she has lost her mind.
You mentioned you had ideas already about what to include. To get started, picture your scene. Where is Lady Macbeth? Write brief stage directions describing where the action is taking place. What kind of mood is she in?
Jump right into the dialogue. Keep the sentences short and crisp. Is she worried about her husband’s state of mind? Is she happy with the way things have turned out? What is she afraid of? Is she speaking to someone else about any of these issues?
Remember you are essentially writing a conversation that reveals something about Lady Macbeth or moves the plot along somehow.
Soliloquies generally are supposed to be the inner thoughts of characters. What could Lady Macbeth be thinking that she might not say aloud to another character? Is there a particular issue she is struggling with?
Remember, too, that your scene comes before she goes insane. Are there any hints in what she says that foreshadow what is happening to her?
To sum up, begin with general scene setting, bring on your characters, and then write down what the two characters are saying to each other. When Lady Macbeth has her soliloquy, express her most secret innermost thoughts and feelings.
Most of all, enjoy the assignment and have fun. Lady Macbeth is one of the most famous, complex characters in literature.