You can download your account settings as a JSON file. That includes the lists of followed communities, saved posts and comments, and blocked instances, communities and users. I'm not aware of any other way to download additional data.
I will add, as a disclaimer, that I have not checked if that as Nutomic highlighted below, there are conditions (password change, etc) under which any or all JWT (user, instance, etc) become invalid. So do audit the code if this is something that concerns you. As far as I am concerned, I treat the JWTs as extra-sensitive information, and store them only on machines I own.
Edit: correct information in the light of Nutomic's comments.
Account settings import/export exists, but not a full data export. Part of the reason is that importing and overwriting historical data isn't possible with activitypub.
But at least a full data export would be possible to do. Open up an issue for this in the lemmy back end.