Having declared a mental health condition in the past, how will this affect my plans to work as a pilot, and what should I do about it now?
This answer is inspired by best-practices in dealing with immigration officers.

I shall not dance around your feelings.  You picked the right industry to tell that lie, because the airline industry in particular is extremely familiar with fraudulent "support animals" - people slapping a vest on Fido to sneak them where pets do not belong.  The airlines have struggled with this and its consequences, and the FAA is certainly well aware of it. 

Simply Tell The Truth about your mental health.  Which is to say, tell the truth now. 

But you can't tell the truth if you don't know what is is. At extremes, stating a fact you don't know is lying, because you imply that you know it.

The form asks if you were diagnosed with a mental disorder.  Note those words. 

The origin of the question on the matter is the "doctor"'s letter.  Review it.  If it plainly claims "diagnosis" and "mental disorder", then that is that: you must tick "yes". However if it is ambiguous on the point, then you don't know -- you should ask the "doctor" for clarification. I would write them and say you are applying for an ATP license, and ask them a) Did you diagnose me?  If so was the diagnosis of a mental disorder in the meaning of this form (attached)?

And the doctor will write you back and state definitively a) whether it was a diagnosis and b) whether it was of a mental disorder or other reportable thing on that form.  She will surely give you the most helpful answer possible within her medical ethics. You may rely on that because she is a licensed professional.  There may be an ethical issue there, but that's between her and her medical board: not your problem. 

"Ah, but she can't recant the diagnosis since she's not a bona-fide doctor!"  Well then, she also was incapable of issuing a diagnosis, so you were not diagnosed after all.  

If FAA asks about the contradiction between your FAA claim and your support animal letter, show them this second letter.  Of course they will suspect your goal was to cheat your landlord, but that does not violate any FAA regulations (except perhaps the "morals" rule, but therein, they are concerned about serious arcs of behavior that indicate disrespect for the duties of pilot, e.g. lying to FAA about mental health, not lying to landlord about a cat).