For example, "Lucy and I are going to a movie" vs. "Myself and Lucy are going to a movie" vs. "Lucy and myself are going to a movie"
The reflexive pronoun should not be in the subject of a sentence unless it is used as an intensifier, accompanied by another noun or pronoun:
I, myself, am going to the movie.
In the above, the sense conveyed might be: I'm not sending someone else to the movie [to write a review], I'm doing it personally!
This isn't the case in your example, so the correct choice is:
Lucy and I are going to the movie.