What does the following sentence mean?

To labour under an illusion is to hold an idea on an issue and to work and live holding onto that idea. For instance, spy movies are full of what might be called "unwitting accomplices" - people who think they are acting on behalf of a good goal, only to find out that they are in fact acting on behalf of a bad goal. That type of thing is labouring under an illusion.

Usually, it's only when the illusion is revealed do we know that we've been labouring under one (and so the phrase is usually associated with finding out about the illusion).

The phrase on that account is usually meant to indicate a specific person or issue. Don't change your plans on my account is one way the phrase is used.

Putting these together then, what I'd expect this to mean is to have someone realizing that they've been labouring under a false idea concerning some sort of idea or person.

For instance, I can say something like:

I've been working for this company for years, assuming I'd be promoted to partner at some point. Well, I just found out that I'm never going to get that promotion. I guess I won't be labouring under any illusions on that account any more.