My elderly mother's mortgage still has the original interest rate of 14%, since the 1970s. Is not lender obligated by law to reduce it? Can she have it refinanced even though she is not working?

Most likely not, unless the loan is adjustable (and I do not believe that there were adjustable mortgages in the 1970's).

Although your mother is not working, that does not mean she does not have income. Social security, pension income are just a few things that are used.

Since most mortgages have 30 year terms, your mother's is close to being paid off. You might want her to discuss a rate modification with the lender rather than burdening her with another long term mortgage.