My daughter has an apartment lease, but has an exacerbated mental condition where it is no longer safe for her to be living by herself. It has been recommended by her doctor that she relocate into a living arrangement with other individuals. Can a letter of medical necessity break her lease?

No, sorry. What you could do is try to find someone to take over the apartment, and see if they will be accepted. I did that when I bought my house, although I also paid for an extra month and lost my security deposit.

Recommended or ORDERED, has a court declared her not able to care for herself yet ?

Can someone move in and care for her there.

But no there is no law that allows her to break the lease.
If she someone talks to the landlord, he may allow it, with a small penalty, or even none.
If not, she moves, legally she is to pay rent, if she does not, she can hope the judge will give the doctor order some consideration