Possibly the murderer used a mask that looked like Lupin's face to get comfortable with the woman, Francine. All the while, he may have hid the sleeping Lupin in the closet and then put him in the bed when he was finished with the woman.
Or Lupin met the woman before he left for the psychologist's house, and got comfortable with her, but then was knocked out, the murderer struck and altered the footage while Lupin was unconscious.