Snape make a bad break in this conversation. He calls Lily by the surname, says "Lily Potter." In my opinion, this is not an accident, something that Severus began to perceive her not as Lily Evans, but as Lily Potter, says that he accept her along with her husband and child.
But here we are resting on one problem - Snape didn't know that James was animagus, which means that he might not have associated Lily's patronus with him.
By the way, do students teach the Patronus spell? Harry demonstrates Patronus to OWL, this is "aerobatics", he should not know this idea at that time. But probably, they learn later? It is possible that Snape saw James's and Lily's patronus, when they were taught, in the seventh year is permissible.
Or maybe they weren't studied at school at all, and, say, Snape taught Lily to call the patronus. Finally she was so interested Dementors ...