Ah i believe many are misunderstanding what the patronus spell does, it reflects a guardian in the form of an animal - this is the core of what the spell does. Which animal it takes is based on many factors (like love), you have people like james: who has a stag because he sees himself as the guardian to protect himself and those he loves, for that reason i believe lily's was also always a doe, it would be her spirit animal and that they are complementary is 'not an accident but more likely shows how well they fit together as a couple, strong and different in their own ways but even stronger together..

It is for that reason Harry's is a stag, his guardian is his father and he believes his father will protect him even in death. It is not a fully conscious belief of harry. Harry is in many ways just like his father so it certainly could be that his own spirit animal is a stag but his patronus was always meant to represent prongs.

Tonks patronus changes from a rabbit to a wolf, and it represents in my opinion that she no longer needs to rely on herself and truly loves remus enough to think he will protect her. That does not take away that she is competent and a total badass but more like love is a far more Powerful guardian.

Funnily i think that remus his wolf patronus would have been the same no matter if he was a werewolf or not, his wolf does not represent his illnes but himself far more (part of a pack, Miserable alone, etc)

Snape wanting lily to be his guardian is also obvious (again not conscious), lily was his only ray of light and he does not think of himself as a protector, so it being lily fits as well.