1/In book 7 (DH), chap 33 (Prine's tale): When she knew Snape nearly die, she never bother to ask "her best friend any questions. Doesn't ask if he's ok, doesn't ask if he is hurt. Just tells him to be grateful to James.
2/ In book 7 (DH), chap 33 (Prine's tale): when Snape told Lily that the marauders hurt many people, she said: "that's not dark magic, though". This mean, she thought that, if you hurt other people but you use light magic, then this ok? What's wrong with her brain? Dark or light magic are not important, all dark and light magic also can hurt people the same.
3/ Lily Evans could of ended the scene in SWM quickly and effectively if she had just come directing her wand at Severus and said "liberacorpus"! In book 6 (HBP), chapter 16 (A very frosty air) Lupin said that: this spell had a great vogue in school in his 5th years and and used by many students across the school, every students used this spell. So that mean every one knew the counter-curse, include Lily.
but she never save Snape herself, she always distracted to talk to James all the time. She only pretend to want to save Snape, but actually didn't do anything for saving him. While he was choking on the bubbles and possibly dying of suffocation, all the school students can see his bare legs, although she can save him in 2seconds, but all Lily did was talk to the boy she had fantasized about, and nearly smile when she saw him was hanging up-side down and bare legs. I blamed Snape for calling her mudblood, but If you were Snape, I don't think you can say anything good to her after being betrayed like that. If I were Snape, I would have never come to say sorry to her after that. Only Snape is so blind-eyes in love with her.
After Snape called her mudblood, she immediately sneered at him and call him Snivellus, and told him dirty, "wash your pants"
Him calling Lily a mud blood was terrible but what about the idiots who bullied him while he was minding his business sitting under a tree? What about the so called prefect (Lupin) who turned his back on his friends bullying someone? What about the fact Severus went back, and pleaded for forgiveness from Lily?
4/In the letter she sent to Sirius in book 7, DH, chapter 10 (Kreacher's tale), when Petunia sent Lily a Chirstmas present, she sneered and called this present: "horrible vase", and let Harry smash this present. Lily was a very "good" sister, then?
5/ in  In book 7 (DH), chap 33 (Prine's tale): From the scene at the Portrait when Snape try's to apologize she says she has "Made excuses for him for years." But in what way does that help him? It doesn't. It helps her. It makes her look good to her fellow Gryffindores and turns Snape into a charity case. She knows Snape is abused at home. She knows he is bullied at school. And she said: "I can pretend any more". From a very long time, she didn't consider Snape is her friend, she just waiting a chance to dump him so she can officially date James.
6/ All that being said though, one of the biggest flaws I see with Lily Evans, something I see with a lot of Gryffindors in the series, is their inability to see the world in anything but black and white.
In book 7 (DH), chap 33 (Prine's tale): Lily tells Severus to stop talking to Mulciber and Avery. And risk getting hurt? Lily knew that Snape share a dorm room with Mulciber and Avery, and Mulciber and Avery are very evil. So, if Snape stop talking to them, he can be hurt when he sleep. He will not only be bullied when he is outside the dorm by the Gryfindor, but also in his dorm by his dorm mates. Did Lily too naïve or she cannot think logic?
7/ she was friends with and married a bully. She was friends with four boys/men that were horrendous bullies. She had five solid years of witnessing what absolute unrepentant monsters they were to her "best" friend. I could never and would never associate with anyone who I witnessed treating another that way. To date and marry that monster says she was as evil inside as he was. Lucius loved Draco but he was still a evil character. Sirius loved Harry but he was even up until death still a evil character. They both still treated anyone and anything different from them as scum beneath their feet. It's like those people who say they find religion and supposedly are now good people, that does mean you should have anything to do with them.
8/In Book 7, chap 33, when Lily told Petunia that she knew about the letter Petunia wrote to Dumbledore, and when Petunia got angry, Lily blame Severus: Severus found it, not her. How can Severus dare to go to Petunia's room?
9/ Lily wanted to be part of this wonderful world and she had to dump Severus to do it, get rid of him and marry up to the well established Old family of Potter.
Lily was never going to be able to be the social climber she wanted with racism so rampant about muggleborns without a rich named family behind her. That's why she suddenly was in love with the guy she called a toerag. She was talented and was probably the reason Harry survived but the vision of Lily as some icon of goodness and love is a joke. I could never befriend the people who are assaulting my friend, even if we weren't friends anymore.
10/People always think that: because Lily sacrificed her life for Harry => she is good person. Narcissa and Petunia can sacrifice their life for their children, too.