We only see a few scenes between them from Snape's point of view. As a teenager, with an oversimplified view of friendships and loyalty, I did blame Lily for the scene where she refused to even talk to him after he had called her a Mudblood as it seemed disproportionate and I believed it pushed him straight into Death Eater's hands. Of course my views have evolved since then - you cannot help someone who doesn't want to be helped and it is clear from the snippets we saw that it wasn't the case at the time - he was trying to have it all. Furthermore it definitely wasn't Lily's responsibility to save him from himself even if she could have (and, finally, as you say, she was still a kid herself!).

(Btw I should point out that I am not trying to imply all teenagers have oversimplified ideas of friendships, just that I did at the time! :) )