I shall just add in that young Sev expected that Lily could sort into Slytherin - apparently based on talent.
Well, taking interview and extended canon (Beedle) into consideration, Lily could sort into Slytherin.
We know from Dumbledore's comments in Beedle that Muggleborns have Squib ancestry. There aren't any real Muggleborn witches or wizards. Then there's the infamous Mafalda Weasley, the daughter of a Weasley Squib and a Muggle. If she had made it into the books, she had been a halfblood Slytherin. So if the Hat by unknown magic means knows the real bloodstatus of a student, it could have put Lily or any other so-called Muggleborn into Slytherin. Funnily this should not have caused severe problems with the racist students, because the Hat's decision verifies itself. Slytherin doesn't admit Mudbloods -> sorted into the house anyway means you are at least halfblood -> good enough. Tom Riddle proves the assumptions that the Hat has some ways of guessing bloodstatus. His parents were unknown, he was accepted among his peers anyway.