Snape had a "friendship" with Lily Evans. Other relations are not known. Snaps was friends with Lilly evans but he did have a crush on her

Lily was the only woman he ever loved. Its possible that they would have ended up together if Snape hadn't spent his time hanging out with future death eaters, and then called her a mudblood. After he called her a mudblood, he still hoped that they would get back together at some point, and after she died he felt too guilty to date anyone else. Besides, if you've read any of the books or seen any of the movies, then you know that Snape became the sort of person who nobody would really want to be in a relationship with.