Lilly loved James whose Patronus was a stag, therefore hers became a doe. Snape hid that he loved Lilly for so long, what if Snape's Patronus was a doe because he loved Harry, whose Patronus was a stag?
If Snape did love Harry, it was one case of serious tough love. But I do not think so.
Please recall that Snape used to have periodic strategy discussions with Dumbledore in the Headmaster's office. There was a scene where they spoke of Snape's undying love for Lilly (and clearly not Harry). Snape took out his wand a summoned a Patronus -- a doe.
Dumbledore says something like "After all these years?"
Snape responds "Always."
The "Always" would indicate that Snape is including the period of time before the first meeting of Snape and Harry.
It's likely that Lily's patronus never changed. In fact, it is not a spell that is learned until a wizard older, and they were likely already together by the time she could produce one. Snape's changed to a doe, NOT a stag. If we were to assume that the gender of the patronus matched the gender of the person, then Snape would have changed to a stag, which it did not. If he loved Harry...it would also be a stag. Since Snape's is a female doe and he is a man, then there is no reason to believe that Lily's changed to match James' patronus because they aren't the same patronus. There is also no reason to believe that Snape's patronus changed to match anyone other than Lily's.
JKR only indicates that love can influence the form of a patronus and does not specify how Lily's formed. Perhaps JKR chose to make Snape's a doe to eliminate the confusion that it could also indicate he loved James or Harry. No other characters are mentioned as having a doe patronus.