Interesting that you put this in the "Law & Ethics" category, since what you are asking is neither ethical or legal.
A "doctors note" does not magically turn some mongrel into a "therapy dog", "emotional support animal" or "service dog". Strike out.
If you are lonely, join a club, spend some time reading to kids at the library, volunteer at a Center for Independent Living serving the disabled, go to the gym, drive for Meals on Wheels, or any other number of constructive activities. Do not lie just to get your way when you already know the rules. Doing so would only verify that you do not have the basic human tenets of Honor, Integrity, Courage, or Responsibility.
Husband of guide dog user who has her guide because she is disabled, not because she is "lonely".