If the Lie is true, then it's not really a Lie, is it? So you probably have some problems to solve...
The Lie is part of your character's journey or arc so it actually needs to be a lie for it to do its job in the arc.
How does your character solve their problems? What do they finally realize that sets them free? That'd be the Truth of the story and the belief that kept them from realizing this is the Lie.
In order to make a good protagonist, one important ingredient is to give them some backbone. Whimps are seldom good protagonists. At least not for the whole book. They need to toughen up (physically/mentally/professionally) and break their chains (or die trying—also physically, mentally, or professionally).
Or they risk not being particularly fun to read about.
I'd probably change the narrative in some way to make it possible for the character to, at least, escape from this toxic situation.
The Lie is also intimately connected to your theme or message, so in this case, the theme/message might be that there are some situations (all situations?) where you're helplessly being hated by everyone.
It may be a hard message to get your readers excited about... They will probably ask questions like, what does the character do to fix this? How does he survive this? Why? Why not? Readers want some kind of answer even if it is that there are questions that have no answers, but then they need to feel that in their bones.
You could, of course, also write a character that doesn't follow a positive change arc. But even in that case, there's a Truth that escapes them in some way finally leading to their undoing. And this undoing comes about because they believe in a Lie.
Also, the Lie and the (Emotional) Wound do not have to be the same thing. The Emotional Wound usually gives rise to the Lie. While believing in a lie can be wounding enough, the actual Wound is the root cause. (Check the list on the supplied link for examples of wounds and the lies/false beliefs they give rise to).
This isn't your story's antagonist, is it? It may be hard to give them a change arc, at least a positive one.
You might get away with giving them a negative fall arc (the character believes in a Lie and ends up believing in an even worse Lie) or a corruption arc (the character believes in a Truth but gets corrupted and starts believing in a Lie).
However, in my experience, it's really hard to not make the antagonist's fall take away from the protagonist's win, and ultimately make the story either confusing or the message/theme seem diluted. But maybe better writers than I can do better work in this regard...