"Some boys take a beautiful girl, and hide her away from the rest of the world..."
This review will contain spoilers.
First and foremost, a note about the film's ending. Lisa does not use the term "Anomalisa" in the final scene of the film, but rather says that she looked up "Anomarisa," in a Japanese-English dictionary and that it translates to Goddess in Heaven. Now, "Anomarisa" isn't the Japanese phrase for Goddess of Heaven, though the actual term is a rather similar sounding phrase (Ama Terasu) and the origin of this term makes sense in the context of the film's themes. Ama Terusu (or Amaterasu Omikami) is "the Great Goddess Spirit Shining in Heaven.... Disgusted with her brother because of his violence toward women, Amaterasu enclosed herself in a cave and refused to come out. Eight hundred deities gathered outside her self-made isolation and tried to lure her out with a loud celebration...." Then again, Lisa quickly declares that she doesn't think of herself in this way (as a Goddess of Heaven), and the "mispronunciation" of the phrase renders the ending even more ambiguous.
Furthermore, in the film's final scene, Lisa's voice has returned to its original sound (the voice of Jennifer Jason Leigh), and when she glances over at Emily, Emily no longer has "the common face" (or The Face of Everyone Else); she has an individualized face. I believe that this scene is essentially confirming Lisa's existence. We spend the entire film inside Michael's head, experiencing the narrative from his perspective -- to the point some have claimed Lisa never actually existed and was a manifestation of his psyche. This point, while not being one that I agree with, is supported by exchange near the end of the film between Michael, his wife and his son. Michael's wife notices that the Japanese automaton is dripping semen; this hints that Michael actually may have had sex with the doll (rather than Lisa) because 1) sex dolls usually don't just drip semen for fun and 2) if it isn't his semen, then whose is it? The automaton is an antique which was just purchased, and if the bodily fluid is as antiquated as the automaton, it wouldn't... have the same consistency (I tried to put that as nicely as possible).
However, as I mentioned, the final scene is an important departure from Michael's perception -- he is in every scene of the film aside from this one -- and, to me, proof that Lisa does indeed exist. Rather than viewing this detail concerning the doll as evidence that she was a non-entity, I view it as evidence that Michael may have "engaged" with the doll prior to hearing Lisa's voice. Yes, the automaton may have the voice of Jennifer Jason Leigh and may be cracked in the same location as Lisa's scar, but that doesn't mean that Lisa never existed, that it was only ever the automaton. In my opinion, this is instead an expression of how Michael is replacing something human with something mechanical, something without the ability to regress and change and grow, without the ability to gradually drift away into the singular entity that is the sea of Everyone Else.
Michael is something of an antihero, rather than a protagonist, but the amount that I sympathize with his character, upon each viewing, shifts (from not at all, to a little, to some, to more than expected, etc.) and I really don't have more to say about this point than I already have. His character can be described as anything from merely a narcissistic womanizer to a damaged, lonely, desperate, self-destructive (and consequently destructive) man whose behavior is reflective of having a spent a life chasing something that he's beginning to realize never existed at all. There are many different ways to view his character, and the film surrounding this character has been described as "the most human film of the year." I agree with that statement just to an extent, in that I would only back it if one was utilizing it to describe the way in which Anomalisa addresses every aspect of human behavior, from the tender to the ruinous.
The name of the hotel in which the story takes place is the Fregoli; in psychiatry, the Fregoli delusion -- named after a 1927 case of a woman who believed actor Leopoldo Fregoli was imitating all the people in her life -- or the delusion of doubles, is "a rare disorder in which a person holds a delusional belief that different people are in fact a singular entity who changes appearance or is in disguise." (The paranoid aspect of his delusions, and even potential delusions of grandeur, are addressed during the elongated dream sequence following the sex scene.) His delusions and offset of prosopagnosia are, however, utilized more metaphorically than literally within the film.
Lastly, I admire the film's commentary on human beings wearing masks rather than having faces -- again a metaphorical statement, rather than a literal one -- for that is what Michael does, and what many human beings do. Kaufman utilizes the idea of customer service and the behavior associated with it to represent reality and relationships: simulation of social interaction, a faux reassuring/pleasant voice, artificial smiles and fabricated fascinations. Rules dictating how you're supposed to act, rather than natural action. Michael has mastered these fabrications (and is fully aware how to use them to "increase productivity" in the workplace), but they're not applicable to true and honest human interaction. I believe this point is most notably explored during Michael's speech towards the end of the film, the content of which doesn't matter as much as what it is representing. The scene may feel like an unfocused, stream-of-consciousness rant, but in truth it is symbolic of a man struggling with which face he's meant to reveal to society: his usual mask, or the skin hiding beneath.
"In a dream, you came and held my hand; our love was perfect in that sphere. No, I never met you, my sweet dear. And my friends, they say you don't exist. But friends are cowards, full of fear, afraid to look at what they missed."