It is interesting that Nabokov himself was deeply distrustful of the field of psychology, and this is something that is shown through the contrast between the foreword of this novel, written supposedly by a leading academic in the field of psychiatry, and that Humbert's account, which at every turn mocks and points out the inconsistencies of psychiatry, in particular highlighting the shortcomings of Freudian approaches. For example, consider the way that Humbert rather sardonically records the mistaken conclusion that Pratt came to concerning Lolita's sexual experience. She diagnosed Lolita as being "sexually immature," whereas of course she was very sexually active with her stepfather. Nabokov seems to do his best to discredit psychology as a field as part of his attempt to challenge the reader's view of Humbert: he cannot be labelled "insane" by a system that is flawed in so many ways, and thus is to be regarded as unique, albeit with many difficulties and problems.
It is perhaps therefore suggested that if Humbert had been cured by psychiatry, which, for the reasons stated above, would have been impossible, he would lose the aesthetic sensibility he has. Note the following quote, taken from the end of the novel:
Unless it can be proven to me—to me as I am now, today, with my heart and my beard, and my putrefaction—that, in the infinite run it does not matter a jot that a North American girl child named Dolores Haze had been deprived of her childhood by a maniac, unless this can be proven (and if it can, life is a joke) I see nothing for the treatment of my misery but the melancholy and very local palliative of articulate art.
Art is the only recourse that Humbert has to cope with his state and his emotions, and he uses his aesthetic sensibilities to record his story, producing a work of art that, in spite of its provocative and shocking content, entertains and intrigues the reader. If he had been "cured," it is doubtful that he would find such solace in art in the same way.