This is a matter of state law, but I doubt that any state has a law that prevents someone from resigning as the director of a corporation or other organization.  It would require a form of involuntary servitude not favored by the law.

The designation as a “lifetime” director gives her significant protection against an attempt by others to remove her from office, but even that designation might not protect her from removal by a court if she were declared mentally incompetent or had committed a criminal breach of fiduciary duty.  The protection is for her benefit, but should not require her to remain a director if she thinks the organization is going in the wrong direction, or violating laws that could cause her serious personal liability, or is simply tired of the responsibility.

I would treat her action as any other resignation. I would accept it and relieve her of her board responsibilities. You will have to reflect it on the Form 990-PF you file for the current year when you list the officers and directors. If you are a foundation that solicits new funds and has to file charitable solicitation registrations, your renewals will also need to reflect the change.  If your state requires periodic administrative filings to retain your active status, it may be required on those forms as well.  If you have grantees who specially identified with her, you may want to give them some notice, especially if you don’t expect to continue their funding.  But I don’t think you need to put out a press release or make a big public statement, unless you want to.  For most of the world this is not a big deal. 

If she wants to publicize it, she can do so.  Unless you have a very unusual agreement with her, you can’t stop her, but you ought to have a non-pejorative statement available if you get asked about the situation.