Maybe Snape did something that went against Lily's expectations or values, and she uses the howler to express her disappointment. For instance, he might have joined a group she doesn't approve of.
Well, sometimes it's because he did something really naughty or broke a major rule at Hogwarts.
He might be initially shocked. After all, getting a Howler is a very public and embarrassing thing. He could be so ashamed that he immediately hides away to read it privately, his face turning red with a mix of anger and humiliation.
It might be because Snape said or did something hurtful to Lily's friends. Lily is a loyal person, and if Snape insulted or harmed her friends in some way, she would be furious enough to send a Howler. In the context of fanfiction, there could be a new character introduced who Snape treats badly, and this angers Lily.
In some fanfictions, Snape might focus on his teaching and find purpose in mentoring students. He could also start to explore new friendships within the wizarding community, like with some of his colleagues at Hogwarts.
It might happen if James doesn't follow Harry's instructions or does something dangerous. Like when he experiments with forbidden magic or disregards Harry's warnings about certain magical creatures.
Maybe it happened because he made a big mistake in a magical experiment or broke a strict school rule. That might have triggered a howler being sent to him. The possibilities are endless in fanfiction!
Hermione could be the sender. If Snape has made some unfair judgment in class against Gryffindor students, Hermione, with her strong sense of justice, might send a howler to him to voice her protest.
In many fanfictions, Harry might send a howler when he's really angry or wants to make a bold statement. It's usually a dramatic moment.
Maybe Snape uses an ancient magic spell he's discovered to heal Harry. This spell might have specific requirements or incantations.
The fanfiction usually shows Snape being quite shocked and embarrassed when he gets the howler. It might lead to some interesting character developments and interactions.