Do you think Snape's doe patronus suits him as a character without taking Lily into account? I personally think it comes from a place that's full of beauty and goodness, the same place where his lullaby healing spell comes from. The doe symbolizes grace and gentleness among others. I can't help but think of his gliding walk, his billowing robes, the way he describes potions. I think of how he gently wipes blood from Draco's face, how he lays people in stretchers in POA. It suits him very well.
I can’t honestly say I’ve ever thought about it, but I enjoyed reading your take on it.
I suppose I’ve always headcanoned that Snape had a different patronus prior to the doe, and I’ve always seen the doe as Lily’s - and the change of patronus almost symbolises the death of what Snape used to be.
However, I think that just joins on to what you said. We don’t know when Snape created his healing spell for Sectumsempra, but I quite like the idea that it came after his defection; I like the idea that he himself became more aligned with the ‘good’ of his patronus…that the wannabe Death Eater who had a different patronus might never have seen the worth in the healing spell, but the man he becomes does.