It would be extremely unlikely that Lily was sorted into Slytherin, or that she's an heir. Dumbledore told Harry LV was the last remaining heir of Salazar, though it must be noted that he could have been trying to spare Harry a burden at the time. He probably would have admitted it to Harry at the end of OotP. Besides, that plot has been done already in Dune where Paul Artredies discovers he (and his mother) are Harkonen decendents (house Artreties traditional enemies).
The more telling arguement in favor of her not being in Slytherin is that Snape refers to her as a "Mudblood". The sorting hat specifically mentioned that Slytherin qualities include the selection of purebloods.
There are some interesting ideas about Lily's family to speculate on though. First, while Dumbledore told Harry Petunia was Lily's last remaining relative, "Big D" and his gang beat up a Mark Evans. While Evans isn't exactly an uncommon last name, it seems too much of a coincidence. Second, I have an idea which may explain a lot about Lily's family and Petunia's attitude. Suppose both of their parents are Squibs? It would explain why they were so happy that Lily turned out to have magic, and why Petunia is so bitter about it. It would also explain the knowledge Petunia has about the magical world - she could have been told a lot of bedtime stories and have a lot of talk about the wizarding world after Lily went to Hogwarts. It would certainly explain why she knew about Azkaban and the dementors - and much, much more.