Tough question. Lord Byron definitely did not write "She Walks in Beauty" with Freud's psychoanalysis in mind. Freud and his theory weren't even around at the time. I'd like to say that Freud's theories are simple, but I don't think Freud would be happy with that. I'll try to summarize it in a nutshell. Freud said that the mind can be broken down into parts. Mainly conscious and subconscious. The two come hand in hand, although the two may be in conflict with each other at times.
"She Walks in Beauty" is a poem about a beautiful woman. Bryon plays around with light and dark a bunch in the poem, which are opposites to each other. The conscious and subconscious could be considered opposites to each other. But unlike the tension that exists between the conscious and subconscious, there is no tension or disconnect for the woman being talked about. Her outer beauty and inner goodness are in harmony with each other. The outer beauty could be the visible conscious and the inner goodness could be the subconscious. The reader knows she has good moral character with this line:
"Where thoughts serenely sweet express
How pure, how dear their dwelling place."
The reader also knows that in addition to her good looks and solid moral character, she is a woman that is at peace with herself. All parts of her mind are in harmony.
"A mind at peace with all below,
A heart whose love is innocent!"