Is it ethical to use a recommendation letter from a deceased professor?
If I cared enough about a person to write a letter of recommendation, I would be pleased to think that one day after I am gone that the person could use my letter for their benefit.

You will possibly benefit from this recommendation and possibly someone else will suffer if you are selected based upon the recommendation; however, competition is not generally considered unethical.

There are no legal questions raised that I can imagine.

It seems unconventional, but not extreme.

My feelings are that it would be ethical to use the letter.