It will take some warming up for sure. I think Snape has had so much animosity for Harry for so long, he will have to get past that. I think it will be easier for Harry to get past that.

People have dropped tons of hints about what James and Lily were like, but the people that knew them at school were really James's friends first. Severus was Lily's friend. He could tell Harry so much more about Lily than about her eyes.