Lily hadn’t gone into her Sorting at eleven wanting to be placed in Slytherin. She hadn’t gone into her Sorting really wanting to be placed anywhere in particular, although if anyone had asked her, she would have automatically said Gryffindor, foregone conclusion that it was. Most everyone she had spent her childhood loving or annoying or following around in hero worship was in Gryffindor, so that’s where she would probably be too. When the Sorting Hat slid over her eyes, her body was already pointed towards Gryffindor, ready to join her brothers and cousins as soon as she received the proper confirmation.
It didn’t take long for the whispering voice in her ear to tease out the fact that she wanted to make a name for herself in her own right, that even though she loved her family, she didn’t understand why simply being related to them was a reason for people to fawn over her. The hat didn’t give her much warning before shouting out Slytherin. Lily doesn’t have a very firm memory of the moments immediately following her Sorting or the last few names called thereafter. She just remembers refusing to make eye contact with anyone from the Gryffindor table for fear that she would see horror or disappointment on the face of someone she cared about and would start to cry in front of everyone.
Over the years, her feelings towards the Sorting Hat have changed from mild distaste to vague affection. She probably wouldn’t have ever asked for Slytherin, but she can’t argue that it’s exactly where she belongs, and she can’t really hold it against the Sorting Hat for knowing that before she did.