After a month of crisis caused by the deposed shah of Iran's admission to this country for medical treatment, a key question remains unanswered: Was he really so sick that no other country, including Mexico, could have treated him?

The shah's exact conditiion, good or bad, remained a closely held government secret yesterday.

The best available medical sources said he is still basically "a sick man," with a partly or temporarily suppressed histiocytic lymphoma, or lymph gland cancer, that is expected to flare up again.

But some sources say his cancer may have been less widespread than his doctors said after they first saw him in New York.

New York Hospital-Cornell Medical Center, which treated the shah from his admission Oct. 22 until Sunday, said yesterday it would say no more about him. It has said little to date.

On the basis of all the facts known, many doctors now say the shah could have been treated as well in Mexico as in the United States for his cancer and gallstones, a course that might have avoided today's crisis over the seizure of 50 American hostages in Tehran.

Many of the same doctors are also asking why the governmnet apparently took the word of one doctor that the shah, in President Carter's words, had to be admitted to the United States "to save his life," and that not even a diagnosis could be made in Mexico.

That doctor, dispatched to examine the shah by banker David Rockefeller, who had been pressing for the shah's admission, was Dr. Benjamin Kean of New York Hospital-Cornell. Kean is a specialist in tropical diseases, not cancer or gastric disease, at that medical center, which is heavily endowed by the Rockefeller family and includes David's brother, Laurence, as a life member of its hospital board.

A State Department spokesman said yesterday that the department sought other independent medical advice before admitting the shah. But he would not say what doctors were consulted, or when. No American doctor other than Kean is known to have gone to Mexico to examine the shah.

Kean has said he was telephoned by Dr. Eben H. Dustin, the State Department's top doctor, in October, that he gave Dustin a brief oral report and that this was his only contact with any government official.

Dr. Vincent DaVita, cancer treatment head at the government's National Cancer Institute and a world leader in lymphoma treatment, has said he was not consulted.

The shah's New York doctors held their only news conference on Oct. 25. They have issued no statement on the shah's condition or diagnosis since a brief, barely informative one on Nov. 28.

The Washington Post has questioned 12 well-known American specialists, all familiar with Mexican and world medicine, on the shah's diagnosis and treatment and facilities elsewhere. All but three said that, given his illnesses as now known, he could have been treated at least adequately in Mexico City, and several said he could have had excellent treatment there or in several European and Canadian cities.

The Boston Globe last week similarly questioned 10 authorities, with much the same result.

Few doctors were willing to be quoted by name at what they called this "sensitive" time. But most said that:

There seems to be no doubt that the shah was gravely ill, and even in danger of death, if not treated, from two conditions: the lymphoma and serious gallbladder disease.

These conditions could have been fully diagnosed and treated, as they were in New York, at one of two leading Mexico City centers, El Centro Medico or the Instituto Nacional de Nutricion. Both hospitals have CAT scanners (for computerized X-ray diagnosis) and high-voltage radiation facilities, despite recent statements by the shah's aides that such machines don't exist in Mexico.

If necessary, teams of American specialists could have been flown to Mexico City, just as a Canadian doctor flew to New York to remove the shah's last gallstone.

Some cancer specialists maintained that almost no foreign medical centers, and none in Mexico, combine treatment research and general expertise in the same way leading U.S. centers do to give a patient the best chance.

But Dr. Joseph Sokol of Duke University, a specialist in lymphomas, said, "What I've read is that the medical folks in Mexico City are put out at the implication they can't treat a cancer. I can't say that I blame them. They've got good people."

Two Mayo Clinic specialists in gastroenterology said Mexico City has hightly qualified gastroenterologists.

Almost unanimously, the doctors questioned complained, however, that they haven't been told much about the shah, considering, said one, "what we all ought to know" to help set the nation's policy.

"We know we get lied to sometimes," said another. "The lack of facts is disturbing."

The State Department repeated that release of more facts is up to the shah and his doctors, though Air Force doctors are treating him now.

New York Hospital said the shah has ordered silence on his condition. The hospital also said that a patient, "whoever he may be," is entitled to privacy, and that all further questions should be referred to the shah's advisers.