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.
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.
In some fanfictions, Sirius might use it as a chance to show off his independence. He could read the Howler out loud in front of his friends, laughing at his mother's old - fashioned views. This would show that he doesn't care about her threats and is proud to be different from the rest of the Black family.
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.
Snape might be initially in shock. He had trusted Lily deeply, so the betrayal would hit him hard. He could become very angry and bitter, perhaps vowing revenge against her. He might also close himself off emotionally, not wanting to trust anyone again.
He'd probably be shocked at first. After all, getting a howler is quite embarrassing.
However, if Hermione knew she was in the wrong, she might feel ashamed. But still, she would likely try to make amends in a more private and rational way. She wouldn't just take the public humiliation lying down. Instead, she'd approach Annabeth later and say something like 'I'm sorry for what I did, but the howler was too much. Let's talk about this properly.'
He might be initially shocked. Draco is used to being the one in control and having others be intimidated by him. A Howler from Percy, someone he may not have considered a huge threat before, would be unexpected. He could be angry and vow revenge in his mind.
Harry might immediately gather his friends and share the contents of the Howler with them. He values their input and they've always been there to support him. Together, they would analyze the message and come up with a plan. Maybe he'd be a bit angry too, feeling that Voldemort is always trying to disrupt his life and the safety of those around him.
Harry might be initially shocked and embarrassed. A Howler is a very public form of scolding, and in front of all his friends and classmates, it would be a humiliating experience for him.
There are versions where Snape reacts defensively. Let's say Lily confronts him about his actions that seem to be harming her or her friends. He would immediately start justifying himself, listing all the reasons why he did what he did, trying to make Lily see his point of view, even if deep down he knows he might be in the wrong.