Since I have medical standing to break the lease, does she have any legal standing to take my security deposit?
Your security deposit is not germane to your desire to break the lease.
Your landlord doesn't have to allow you to terminate the lease.
However, your landlord is agreeable to allowing you to break the lease IF you agree to forfeit your security deposit.
Again, your landlord could have said, you are free to leave, but you still owe me four months rent.
Furthermore, this is not about anyone's legal standing.
It is about TWO parties who agreed to a contract, which in the matter at hand is a leasehold.
Your landlord could have asked you to vacate the unit four months early because she wanted to allow her mistress to live in the unit.
You have the absolute right to refuse, or to agree to leave the unit IF the landlord paid you $4,000 PLUS your security deposit in FULL.
You are parties to a contract, and only law involved is contract law, your lease.
Should I fight for my security deposit?
What you decide to QUARREL over is up to you.
If you wish to squabble over the return of your deposit in FULL, but voluntarily decide to vacate the unit because of YOUR medical issues is of no legal moment or import to your landlord.
Your landlord is rather gracious to even consider allowing you to break the lease.
If my health was at risk, I'd eagerly forfeit my security deposit to aid me in a full recovery.
What you choose to do is entirely up to you, mate.
I wish you improved health, good luck.