First you said buy out was 24K than you said it was 14K. That could make a difference. With a lease she could turn in the car and get a new one, downgrade for things not necessary, and have a brand new warrantee.
I leased my present car and because I really liked it, I bought out the lease at the end and financed the buy out. Now the warrantee is about to expire and I realize my mistake. Now I have payments close to equal to what my lease payments were and now in order to have any help with mechanical problems I have to pay around $100 per month for an after market warrantee. (Ouch) I could have turned it in, had a new car and another full warrantee for about the same thing I paid for the original lease.
I was 75 when this happened and I was aware of my mortality but for some reason (can't blame intelligence) I bought it anyway. Your Mom is in her 80's and odds are that it might indeed be her last car. If however, she can pay off the buy out without a loan, then either one will work. What happens if she were to pass before the lease was complete, the estate is protected from pay off of a loan and her estate is free of depreciation value loses. My opinion and or advise is get the best deal you can on a lease and do the simplest thing, Lease! However, if she can easily pay off the lease then a buying a new car is also close to the same thing.