What animal would Lilly's patronus ahd been?

A doe, because she was in প্রণয় for James. In the last book, Harry says that Snape had a doe patronus because he did প্রণয় Lily. So probably Lily patronus was a doe

A doe, as stated in the last book, as it represents her প্রণয় for James-who's an animagi stag. Snape also has the same Patronus, as he was in প্রণয় with Lily.

It's confirmed to be a doe (in the 7th book) but I don't think hers changed because of her প্রণয় for James. It'd have been weird for Snape's to change reflecting hers if hers was already a reflection of someone else's. I think hers just happened to be a doe.