There are a couple of common representations of Lily in fan fiction.
- She is a money/power hungry person who married James because he was a rich pure-blood.
- She was drugged by James, who unscrupulously used love potions.
- She would have left him as soon as she was uninfluenced.
- In some of these stories, she is legally trapped in the marriage, but she manages to have an affair, such that Snape is still the biological father.
- She was super intelligent and James was an utter moron.
- If the first assumption is also true, she tolerates this because she needs the family name/wealth.
- If it isn’t, then she might not have realised it until she sees him squandering that wealth in blind obedience to Dumbledore.
- He might recognise this and put her in charge.
More rarely, you see one or more of these subverted, for example she blindly follows Dumbledore while James is more suspicious. It is exceptionally rare to find a positive representation of both Lily and James. I find none of these biases acceptable in a story, and will strongly consider abandoning that story as soon as I come across them.
What is acceptable is that James, while inteligent and responsible, recognizes that Lily’s non-magical background provides a level of insight into a previously untapped muggle economy. He, with a hereditary fortune at a time of war and turmoil, might leverage her familiarity with the non-magical world to diversify in ways no other pure-blood can.1