You should start using paragraphs, that way it will be easier to read, which will keep your readers. Your grammar is good enough.
You also kind of just jumped straight into the story, without telling us anything. It's okay to be mysterious, or if you have planned to reveal more, then don't let me stop you. If not then I think you should tell us more, about the characters, and what has happened previous years. Like how did Lily and Izzy become friends?
Also tell us more about how they feel. You are doing a great job, just show more emotions. Like was Remus anxious, that she knew his secret. We certainly see Lily's emotions though.
I like how you portray Remus so far, I think you should have him express how he feels more, and make him more stubborn. He seemed okay with Izzy knowing of his condition. In most fanfictions he gets angry.
James and Sirius are perfect! Lily seems a bit mean though. Could you make her a bit nicer, she is even mean to Izzy.
You haven't really mentioned Peter either. You should add a few more characters, so it's not just limited to them. If there is more characters, there will be more action, they could also be the cause of conflict.
I like the fact that Izzy is different, it offers a lot of possibilities. I like the way she can tell the future. It's an interesting twist. It could also be her downfall. There is also the possibility of her having more unusual powers.
Keep in mind all I have said. You are off to a great start! Keep it up, it's got a lot of potential✅
Much love⭐
-Always_a_slytherin